science;ilpac unit s2: atomic structure

UNIT

INDEPENDENT LEARNING PROJECT FOR ADVANCED CHEMISTRY

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UNIT

~

Atomic Structure

S2-A

© Inner London Education Authority 1863

First published 1863by John Murray (Publishers) Ltd50 Albemarle StreetLondon W1X 4BD

Reprinted 1984~ 1985

All rights reserved.Unauthorised duplicationcontravenes applicable laws

Printed and bound in Great Britain byMartin's of Berwick

British Library Cataloguing in Publication DataIndependent Learning Project for Advanced

ChemistryAtomic Structure. - (ILPAC; Unit S2)1. ScienceI. Title II. Series500 0161.2

ISBN 0 7195 4036 4

ii

CONTENTS

PREFACEAcknowledgementsKey to activity symbols and hazard symbols

INTRODUCTIONPre-knowledgePRE-TEST

LEVEL ONE: THE NUCLEUSRELATIVE SIZESHow big is the nucleus?ATOMIC NUMBERI MASS NUMBER AND ISOTOPESIsotopic symbolsTHE MASS SPECTROMETERInterpreting mass spectraCalculating relative atomic mass of an elementMass defect and binding energyRADIOCHEMISTRYTypes of radiationNuclear reactionsNuclear stabilityTHE RATE OF DECAY OF RADIOISOTOPESRadioactive datingARTIFICIAL TRANSMUTATION OF ELEMENTSUses of radioisotopesLEVEL ONE CHECKLISTLEVEL ONE TEST

LEVEL TWO: ELECTRON ARRANGEMENTSINTRODUCTIONIONIZATION ENERGYExperiment 1 - estimating the ionization energy of a noble gasSuccessive ionization energiesIonization energies and the arrangement of electronsModels and their usefulnessWave-particle dualityTHE ORBITAL MODEL OF THE ATOMOrbitalsHow many electrons per orbital?The shapes of orbitalsThe number and type of orbitals in an electron shellThe arrangement of electrons in orbitalsThe aufbau principleBoxes-in-a-rowUsing a noble gas 'core'The 81 PI dl f notationUSING IONIZATION ENERGY VALUES TO IDENTIFY AN ELEMENTFirst ionization energies of successive elementsEMISSION SPECTROSCOPYExperiment 2 - using a hand spectroscope to observe emission spectraWhy do atoms emit light?

iii

vvi

vii

1

23

5

55689

11121517171921222424272829

33

33333438394142434344444648495151525657596062

The visible part of the hydrogen emission spectrumThe complete hydrogen emission spectrumConvergence limits and ionization energyLEVEL TWO CHECKLIST

64666870

END-OF-UNIT TEST 73

APPENDIX ONEA HISTORICAL PERSPECTIVEChronological table of some important developments in atomic theoryDalton's atomic theoryThe discovery of the electronThe Geiger-Marsden experimentMoseley's experimentConsolidation

79798081818182

APPENDIX TWOThe relationship between charge and energy 83

APPENDIX THREEADDITIONAL EXERCISESCalculating relative atomic mass from percentage abundance

8484

ANSWERS TO EXERCISES 85

iv

PREFACE

This volume is one of twenty Units produced by ILPAC, the Independent LearningProject for Advanced Chemistry, written for students preparing for the AdvancedLevel examinations of the G.C.E. The Project has been sponsored by the InnerLondon Education Authority and the materials have been extensively tested inLondon schools and colleges. In its present reVised form, however, it isintended for a wider audience; the syllabuses of all the major ExaminationBoards have been taken into account and questions set by these boards have beenincluded.

Although ILPAC was initially conceived as a way of overcoming some of thedifficulties presented by uneconomically small sixth forms, it has frequentlybeen adopted because its approach to learning has certain advantages over moretraditional teaching methods. Students assume a greater responsibility fortheir own learning and can work, to some extent, at their own pace, whileteachers can devote more time to guiding individual students and to managingresources.

By providing personal guidance, and detailed solutions to the many exercises,supported by the optional use of video-cassettes, the Project allows studentsto study A-level chemistry with less teacher-contact time than a conventionalcourse demands. The extent to which this is possible must be determinedlocally; potentially hazardous practical work must, of course, be supervised.Nevertheless, flexibility in time-tabling makes ILPAC an attractive propo-sition in situations where classes are small or suitably-qualified teachersare scarce.

In addition, ILPAC can provide at least a partial solution to other problems.Students with only limited access to laboratories, for example, those studyingat evening classes, can concentrate upon ILPAC practical work in the laboratory,in the confidence that related theory can be systematically studied elsewhere.Teachers of A-level chemistry who are inexperienced, or whose main disciplineis another science, will find ILPAC very supportive. The materials can be usedeffectively where upper and lower sixth form classes are timetabled together.ILPAC can provide 'remedial' material for students in higher education.Schools operating sixth form consortia can benefit from the cohesion that ILPACcan provide in a fragmented situation. The project can be adapted for use inparts of the world where there is a severe shortage of qualified chemistryteachers. And so on.

A more detailed introduction to ILPAC, with specific advice both to studentsand to teachers, is included in the first volume only. Details of the ProjectTeam and Trial Schools appear inside the back cover.

LONDON 1983

v

ACKNOWLEDGEMENTSThanks are due to the following examination boards for permission to reproducequestions from past A-level papers.

Joint Matriculation Board:Teacher-marked Exercise~ p70(1977)

Oxford Delegacy of Local ExaminationsExercise 74 (1980)End-of-Unit Test 11(1979)Teacher-marked Exercise, p82(1979 & 1980)

University of Cambridge Local Examinations SyndicateExercise 13 (1977)Level One Test 13(1975)End-of-Unit Test 12(1974)

University of London Entrance and School Examinations CouncilExercises 7(1976), 72(1973)Level One Test 1(N 1977)~ 2(N 1980)~ 3(L 1977)~ 4(L 1982), 5(L 1978) 6(L 1979)

7(L 1979)~ 8(L 1975), 9(N 1975), 10{N 1978),11(l 1980), 12(L 1981)

End-of-Unit Test 1(l 1982)~ 2(l 1982)~ 3(l 1982)~ 4(N 1976)~ 5(N 1975),6(l 1978), 7(N 1978)~ 8(l 1976)~ 9(N 1975)~ 10(l 1979)~13(L 1973)~ 14(l 1981)~ 16(N 1979)

Welsh Joint Education CommitteeExercises 71(1979), 73(1978)

Questions from papers of other examining boards appear in other Units.

Where answers to these questions are included, they are provided by ILPAC andnot by the examination boards.

Photographs are included by permission as follows:

Fig. 8: Albert Einstein - Camera Press ltd.Fig. 13: Mushroom cloud and Hiroshima 1945 - PopperfotoPhotographs of students and Fig. 14: Mobaltron Cobalt Unit - Tony LanghamFig. 25: X-ray and electron diffraction photographs - Alan Mackay, Birkbeck

College

vi

SYMBOLS USED IN ILPAC UNITS

0CO Reading

~Exercise

\\\;l Test

Revealing exercises

~ Discussion

~ Computer programme

'A' Level question ~ Experiment

I[ II Video programme00'A' Level part question

[Q8 Film loop

'A' Level questionSpecial paper

Model-making

Worked example

Teacher-marked exercise

INTERNATIONAL HAZARD SYMBOLS

~Harmful

~Toxic . Radioactive

-.•.

[l] Flammable II Explosive

~

~ Corrosive~

Oxidising1:V ~!&--vii

INTRODUCTION

Elements differ from one another because they have different atoms. Everyatom consists of a central nucleus surrounded by electrons.

In Level One we describe the composition of the nucleus. The nucleus can beregarded as a grouping of even smaller particles: protons and neutrons. Fora given element. all atoms have the same number of protons in the nucleus.but different isotopes of the element contain different numbers of neutrons.We show how an instrument called the mass spectrometer gives us a lot ofinformation about nuclei. We also describe how nuclei decompose (radio-activity) and other aspects of nuclear chemistry.

The total number of extra-nuclear electrons (i.e. electrons surrounding thenucleus) also varies from element to element. In Level Two. we describe howthese electrons are arranged in different shells. and how a shell may haveseveral sub-shells consisting of one or more orbitals. We present evidencefor the way in which electrons are arranged outside the nucleus. byconsidering firstly ionization energies and secondly. emission spectra.

There are two experiments in the Unit - the electron impact method fordetermining ionization energy and a qualitative examination of spectra ofsome s-block elements using a hand spectroscope.

There are three video-programmes designed to accompany this Unit. Their useis not essential. but you should try to see them at the appropriate time ifthey are available.

Instrumental techniques Ionization energy

The hydrogen spectrum

1

PRE-KNOWLEDGEBefore you start work on this Unit you should be able to:

(1) explain each of the following terms:(a) element (e) mole(b) atom (f) the Avogadro constant,L(c) ion (g) frequency(d) relative atomic mass (h) wavelength

(2) state the relative masses and charge~ of the three fundamental particlesin the atom;

(3) describe~ at a simple level~ a planetary model of the atom~ using theterms: proton~ neutron~ electron~ nucleus~ shell (or orbit);

(4) write down the names~ symbols and atomic numbers of the first twentyelements in the Periodic Table;

(5) write dut the electron arrangements of the first twenty elements in thePeriodi~ Table~ using the style: Na - 2.8.1.;

(6) write e~uations for the formation of ions from atoms.

PRE-TESTTo find out whether you are ready to start Level One~ try thefollowing test~ which is based on the pre-knowledge items. Youshould not spend more than 30 minutes on this test. Hand youranswers to your teacher for marking.

2

PRE-TEST1. Copy and complete the following table to summarise the properties of the

three fundamental particles found in an atom.Table 1

Fundamental particle Relative mass Relative charge

proton

neutron

electron (6)

2. Identify the numbered elements in the following extract of the PeriodicTable

Fig.l

Li Be B (1) N 0 F (2)

(3) Mg AI Si P (4) CI Ar

K (5)(5)

3. The electron configuration of magnesium is represented by 2.8.2.Write the corresponding configurations for:(a) Lf t hf.urn,

(b) nitrogen ~(c) silicon. (3)

4. The way in which potassium normally ionises is represented by:+K -T K + e

Write similar equations for the ionisation of:(a) magnesium~(b) chlorine ~(c) oxygen. (6)

5. Explain why neon does not ionise in normal chemical reactions. (1 )

6. Which of the following statements about an atom is not true?The atomic number Z represents:A the number of electrons going round the nucleus~B the positive charge on the nucleus~C the number of neutrons in the nucleus,o the element's position in the Periodic Table. (1 )

3

7. Fig. 2 represents a generalised form of radiation:

Fig. 2.

Which letter represents the wavelength of the radiation? (1 )

8. Radiation is often identified by its frequency. Which of the followingare units of frequency?A cm S-1

B m s-2

C S-1

0 m S-1

E min-1 (2)

(Total 25 marks)

4

LEVEL ONE: THE NUCLEUS

We start this Unit by considering the size of an average atom and the relativesize of its nucleus.

Objective. When you have finished this section~ you should be able to:

(1) calculate the density of an atomic nucleus~ given the nuclear volume~ VN•

RELATIVE SIZESAtomic size obviously varies from element to element. Radii lie within therange 0.05 - 0.20 nm.* The following exercise helps you appreciate how smallthis is.*1 nanometre~ nm 10-9 m (nano comes from the Greek word meaning dwarf).

Exercise 1 Suppose a football~ diameter 22 cm, is scaled upso that it becomes as big as the earth~ diameter13000 km. Calculate whether an atom of diameter0.32 nm will become as big as:A a pin-head~ diameter 1 rnm,

B a 1p piece, diameter 1.9 ern,

C a football, diameter 22 ern,

0 a weather balloon, diameter 1.8 m.(Answer on page 85 )

How big is the nucleus?An atom is small, but its nucleus is smaller still. While the radius of anatom is of the order of 10-l0 m, that of a nucleus is of the order of 10-15m.00 the next exercise to help you appreciate the difference in size.

Exercise 2 If the nucleus of an atom were scaled up to thesize of a pin-head (say 1 mm diameter), how bigwould the atom be?(Answer on page 85)

Since the mass of an atom is concentrated in its nucleus, the nucleus must beextremely dense. Estimate how dense it is by doing the next exercise.

5

Exercise 3 For atoms of elements at the beginning of thePeriodic Table the nuclear volume, V , is givenby: N

VN = 1.73 x (relative atomic mass) x 10-45 m3

Use this expression to calculate the density of the sodiumnucleus:(a) in kg m-3

(b) in ton mm-3

(Answers on page 85)

Were you surprised by the magnitude of this number? The next exercise willhelp you appreciate how much empty space there is in an atom.

Exercise 4 Calculate:(a) the volume occupied by a sodium atom

(radius 0.186 nm),(b) the fraction of the volume occupied by the nucleus.Hint: assume that both the atom and its nucleus are spherical.The volume of a sphere is given by: ~ ~ r3 where r is the radiusof the sphere.(Answers on page 85)

Most of your body is empty space too. If all the spaces between the nucleiwere squeezed out, you would be only half as big as a flea, although yourweight would be the same.

In view of this, you may be wondering why any object appears solid. Theelectrons in an atom move very rapidly around the nucleus, somewhere withina particular radius. The electrons effectively form a shield around thenucleus, marking the limits of the atom's volume and making it seem solid.

You now go on to revise atomic number and mass number and find out more aboutisotopes.

ATOMIC NUMBER~ MASS NUMBER AND ISOTOPESAtomic number and mass number give us important information about an atom andare particularly useful in distinguishing one isotope of an element fromanother.

Objectives. When you have finished this section you should be able to:

(2) define the terms atomic number, Z and mass number, A;

6

(3) explain what isotopes are;(4) use values for atomic number and mass number to calculate the number of

protons and neutrons in the nucleus;(5) use isotopic symbols to describe the composition of a nucleus, e.g. l~C.

You wi~~ have noticed that certain words or phrases in the objectives areemphasised - we cal-l. these keywords. Keywords help you to use the index ofa book to find the re~evant sections to read~ and may a~so he~p you toorganise your notes.

The next task for you to do is some reading. We a~ways identify reading tasksby a symbo~ in the margin - see be~ow. Since this is the first reading taskyou have met in the course so far~ we give some notes of guidance which youehoul.dstudy before carrying out the task.

Read about atomic number and mass number in your text-book(s), andfind out what isotopes are.

Guidance for reading

1. Give yourse~f enough room to work - somewhere you can spread out yourbooks and paper.

2. Go through the objectives ~isted before the reading task~ noting thekeywords. There may a~so be some extra keywords in the reading taskitse~f. (In this particu~ar task~ the keywords in ObjectiVes 2 and 3are the ones to focus on.) Look up the keywords in the index of yourtext-book(s) and note the page numbers.

3. Turn to the page references for each objective and scan* each page in turn~looking out for the keywords. In this way~ identify sections that containre~evant information.

4. Skil~l*each of the sections you 've i.dent-if-ied, bearing in mind what you wantto find out. You know this from the objectives and a~so by ~ooking at theexercises which come direct~y after the reading.

5. Read the passage(s) intensive~y*.

6. Do the exercise(s) which follow the reading. These are designed to testyour understanding of what you've just read~ so you may find that youneed to re-read the passage.

7. Having done the exercise(s)~ look back at the objectives. Do they inc~udeanything not covered by the exercises? If so~ make a note of the missingitems~ under the section heading.

* 'scanning'~ 'skimming' and 'intensive~y reading' were exp~ained in"Introduction to ILPAC: for the Stiudent:"; (Unit Sl: The Mo~e~ p.vii).Look back at this if you aren't sure what we mean by these terms.

7

You should now be able to answer Exercises 5 and 6.

Exercise 5 Define the terms atomic number and mass number.(Answers on page 85)

Exercise 6 Explain what isotopes are and give an example. usingnitrogen.(Answer on page 85)

Now that you have revised these terms. go on to the next exercise. which ispart of an A-level structured question.

At appropriate points throughout the course weinclude questions similar to those you mightencounter in an A-level examination. Thesequestions are identified by symbols in themargin (the letter'S' denotes Special paperstandard).

Where these questions are taken from past examination paper~ the examiningboard and the year are identified in the acknowledgements section at thebeginning of the Unit.

Exercise 7 The table shows the mass number and number of neutrons

~

in the nucleus, for four atoms. W, X. Y and Z.

W X Y ZMass number 36 39 40 40Neutrons in nucleus 1B 20 21 22

(a) Write down the atomic numbers of the four atoms.(b) Which of the four atoms are isotopes of the same element?(Answe rs on p-age 85 )

We end this section by revising a shorthand way of showing the composition ofan isotope.

IsotopiC symbolsYou may already have met a shorthand description of an atom; the mass numberis shown as a superscript before the symbol and the atomic number as asubscript. In this way. I~Al is a description of the aluminium atom. To maKesure that you can use this convention correctly. try the next exercise.

8

(i) Ar (i) Cu (iii) Si

Exercise B (a) Use your data book* to identify the stableisotopes of the following elements:

Describe each one, using isotopic symbols.(b) Write down the number of neutrons in the nucleus of each

isotope.(Answers on page 86 )

*If you haven't used your data book to look up information about isotopesbefcre, try either 'isotopes, stable, abundance' or 'nuclide, abundance' inthe index. Abundance means the percentage of an isotope that occurs innature and nuclide is a general word used to refer to any atom or ion havinga particular nucleus.

In the next section, we look at the mass spectrometer and how it can be usedto find the relative atomic masses of elements with several isotopes.

THE MASS SPECTROMETERIn the first Unit, you learned how to calculate relative atomic mass on thecarbon-12 scale. In this section, you find out how relative atomic mass canbe measured using a mass spectrometer. These instruments are also importantfor measuring the relative molecular masses of compounds, particularlyorganic ones, and determining their molecular structure.

Objectives. When you have finished this section, you should be able to:

(6) describe the principal parts of a mass spectrometer and explaintheir functions;

(7) explain how the deflection of a beam of ions by a magnetic field dependson the masses and the charges of the ions.

If the ILPAC videotape 'Instrumental Methods' is available, youshould now watch the section on the mass spectrometer. Don'tspend time viewing the whole tape at this pointi your teacherwill guide you to the appropriate section.

Whether or not you view the videotape, you should now go on to read about themass spectrometer.

Look up 'mass spectrometer' in your text-book and read the sectionon it, bearing in mind objectives 6 and 7. You may also comeacross 'mass spectrograph'. This instrument works on the sameprinciple as the mass spectrometer - the only difference is theway in which the ions are detected. When you have finished thereading, do the next two exercises.

oITt

9

Exercise 9

Exercise 10

(a) Make a copy of Fig. 3 which is a diagram ofa mass spectrometer.

Fig. 3. The mass spectrometer.

(b) Label the parts A to F.

(c) Describe the function of, or process occurring in, each ofthese parts.


The isotopic composition of the gas radon wasinvestigated using a mass spectrometer, part ofwhich is shown in Fig. 4 below.

i----............. magnetic field<, <, -, / perpendicular

I X to plane of.--~---___ ", diagram

I -" \I "":.~<"~ \

X" \\', \\' \~ \ \

\ \ \\ \ \I \--r--'-~

Fig. 4. detector

(a) Radon has two isotopes, 2~~Rn and 2~~Rn.(i) Write the formulae of the two singly-charged ions thatwould form in the instrument.(ii) state which ion will follow the path marked X on thediagram.

(b) Mention two adjustments that could be made to the instrumentto bring the ions from Y on to the detector.

+If Rn2 ions were to form in the instrument, would youexpect them to be deflected less than or more than the ionsat X and Y?

(Answers on page 86 )

(c)

10

Having established how a mass spectrometer works, we go on to interpret theinformation it records, known as a mass spectrum. You may also find the names'mass spectrometer trace' or 'mass spectrogram' in your reading. These meanexactly the same. Spectrum is a Latin word and its plural is 'spectra'.

Interpreting Mass SpectraObjective. When you have finished this section you should be able to:

(8) identify peaKs on a simple mass spectrum and use them to calculate therelative abundances and masses of ions.

When a beam of ions strikes the detector in a mass spectrometer, it producesan electrical impulse, which is amplified and fed into a recorder. The massof the isotope and its relative abundance are then shown by a peak on a chart.A set of such peaks is a mass spectrum.

Fig. 5 shows a mass spectrum for rubidium. The horizontal axis shows the mass/charge ratio of the ions entering the detector. If it is assumed that ell theions carry a single positive charge, the horizontal axis can also be labelled'mass number'. 'isotopic mass' or 'relative atomic mass'. The vertical axisshows the abundance of the ions. It can be labelled 'detector current'.'relative abundance' or 'ion intensity'.

83 84 85 86 87 88

Fig. 5. mass / charge ratio

Exercise 11 Refer to Fig. 5 to answer this question.(a) Describe the two isotopes of rubidium using

isotopic symbols.(b) What information do you get from the heights of the peak~ on

the mass spectrum?(Answers on page 86)

11

In the next section we go on to use the information from mass spectra tocalculate the relative atomic mass of an element.

Calculating relative atomic mass of an elementObjectives. When you have finished this section you should be able to:

(9) use a mass spectrum to calculate the relative atomic mass of an element;(10) use percentage abundance data to calculate the relative atomic mass of

an element;(11) sketch a mass spectrum~ given relevant data.

We start this section with a worked example~ using the mass spectrum shown inFig. 5. Read through it and then try the exercise which follows:

Worked Example Use Fig. 5 to calculate the relative atomic massof rubidium.

Solution

1. Measure the height of each peak. The height is proportional to the amountof each isotope present.

height of rubidium-85 peakheight of rubidium-87 peak

5.82 cm2.25 cm

Therefore~ the relative amounts of 85Rb and 87Rb are 5.82 and 2.25respectively.

2. Express each relative amount as a percentage of the total amount. Thisgives the percentage abundance.

~o b d amount of isotope x 100a un ance = .total amount of all lsotopes

% abundance of 85Rb ~~5~._8_2~~ x 100 = 72.1%5.82 + 2.25

% abundance of 87Rb x 100 = 27.9%5.82 + 2.252.25

The percentage abundance figures mean that for every 100 atoms~ 72 arethe 85Rb isotope and 28 are the 87Rb isotope.

3. Find the total mass of a sample of a hundred atoms.

Total mass ((85 x 72.1) + (87 x 27.9)) amu*(6129 + 2427) amu 8556 amu

8.56 x 103 amu (3 sig.figs.)

12

4. Find the average mass. This gives the relative atomic mass of rubidium.

total massAverage mass = number of atoms

8.56 X 103 amu100 85.6 amu

relative atomic mass == 185.61

*amu stands for atomic mass unit. 1 amu == 1.660 X 10-27 kg. This value waschosen because it is exactly one twelfth the mass of an atom of the carbon-12isotope, which comprises 98.89% of natural carbon.

Now try a similar calculation for yourself by doing the next exercise.

Exercise 12 Use the mass spectrum shown in Fig. 6 to calculate:(a) the percentage of each isotope present in a

sample of naturally occurring lithium;(b) the relative atomic mass of lithium.

Q)ucco

"0

c::J..0coQ)Olco+-'CQ)

~Q)Q.

4 5 6 7 8

Fig. 6. mass / charge ratio


The next exercise is similar, but you are given data rather than a diagram ofa mass spectrum.

Exercise 13 The mass spectrum of neon consists of threelines corresponding to mass/charge ratios of20, 21 and 22 with relative intensities of0.91; 0.0026; 0.088 respectively. Explainthe significance of these data and hencecalculate the relative atomic mass of neon.(Answer on page 87)

13

You could also be asked to do the reverse of this type of problem - sketch aspectrum from percentage abundance data. Have a try at this by doing the nextexercise.

Exercise 14 (a) Look up the percentage abundances of the stableisotopes of chromium.

(b) Sketch the mass spectrum that would be obtainedfrom naturally occurring chromium. (Let 10.0 cmrepresent 100% on the vertical scale.)

(c) Calculate the relative atomic mass of chromium, correct tothree significant figures.

(d) Label each peak on the mass spectrum using isotopic symbols.(Answers on page 87

You may be asked to calculate relative atomic masses directly from percentageabundance data, as you have just done in part (c) of Exercise 14. For morepractice at this type of problem, turn to Appendix 3, page 84.

The relative abundances of different isotopes explain some anomalies thatappear in the Periodic Table. Find out about them by doing the next exercise.

Exercise 15 When Mendeleev first devised the Periodic Table, hearranged elements in order of increasing relativeatomic mass. In the modern version, elements arearranged in order of increasing atomic number.(a) What would be the effect on the positions of

(i) tellurium and iodine,(ii) argon and potassium,if Mendeleev's system were reintroduced?

(b) How do you account for this effect? (Look up the relativeabundances of the isotopes of 52Te and 531; lsAr and 19K.)

(Answers on page 87

Now try the final exercise in this section which concerns a molecular element.

Exercise 16

Fig. 7.

The scale has beenenlarged for thesetwo peaks

30 40 50 60 70 80mass / charge ratio

14

The element chlorine has isotopes of mass number 35 ~and 37 in the approximate proportion 3:1. Interpretthe mass spectrum of gaseous chlorine shown in Fig. 7, ~~indicating the formula (including mass number) andcharge of the ion responsible for each peak.(Answer on page 87)

The main use of mass spectrometry today is in identifying and analysingorganic molecules which split up to give a great many different ions. Weconsider this aspect later in the course in one of the Units on organicchemistry.

Before we leave the mass spectrometer, we consider its use in explaining howthe particles in a nucleus hold together.

Mass defect and binding energyIn this section we give ~ brief illustration of mass defect and binding energyto hslp you understand the size of the forces in atomic nuclei.

Objective. When you have finished this section you should be able to:

(12) calculate the mass defect of a nuclide, given appropriate masses inatomic mass units.

The mass spectrometer gives such accurate measurements that we now know thesurprising fact that the mass of an atom is slightly less than the mass ofits constituent parts. The next exercise gives you an example of this.

Exercise 17 Use Table 2 to calculate the relative atomic massof a helium atom (~He). Compare this with themeasured value of 4.002588 amu.

Table 2

Particle Mass/amu

proton 1.007 276

neutron 1.008 665

electron 0.000 548


15

The difference between the mass of a nuclide and the combined masses of itsfundamental particles is known as the mass defect. The significance of themass defect is shown by applying Einstein's famous equation describing theinterconvertibility of mass and energy:

E = mc2

Fig.8. Albert Einstein 1879-1955

where E energy, m mass and c = speed of light.

The energy corresponding to the mass defect, calculated using this equation,is known as the binding energy. A very small mass defect corresponds to ahuge binding energy, beca~se c2 is such a large multiplying factor. Theenergy associated with the addition or removal of electrons is small bycomparison, as you see in the next exercise, so that binding energy isessentially an indication of the very powerful binding forces holding thenucleus together. Indeed, both mass defect and binding energy are sometimesdefined in terms of the nucleus alone.

Exercise 18 (a) Calculate the binding energy for one mole ofhelium atoms, using your answer to Exercise 17.(Hint: express the mass defect in kg and thespeed of light in m S-l, so that the energyis expressed in kg m2 S-2; you can easilyconvert tc J and kJ because 1 J = 1 kg m2 S-2.)

(b) The energy required to remove all the electrons from onemole of helium atoms is 331 kJ. What percentage of thebinding energy is therefore associated with the electrons?

(Answers on page 87

It has long been the dream of scientists to make the binding energy of thenucleus directly available for Man's use in a controlled way. We do usebinding energy indirectly, of course, because it is released in nuclearreactions in the sun, where helium nuclei are formed by the fusion of hydrogennuclei (i.e. protons).

From the last exercise, you can see that the fusion of four moles of hydrogeninto one mole of helium releases approximately 2.7 x 109 kJ. By contrast, thecombustion of four moles of hydrogen, a more conventional energy source,releases only 484 kJ. Clearly, there is plenty of energy available if onlywe can learn how to harness it.

16

Image removed

Energy is not only associated with fusion processes but also, to a lesserdegree, with fission, i.e. the splitting of nuclei. Some nuclei split upspontaneously releasing energy in the form of various types of radiation.We consider these unstable nuclei in the next section.

RADIOCHEMISTRYRadiochemistry is the study of reactions involving changes in the nucleuswhich result in the emission of radiation (radioactivity). Many nuclei areunstable and disintegrate spontaneously, especially those of high atomicnumber; all known isotopes of elements where Z is equal to or greater than83 are radioactive. In addition, there are radioactive isotopes of manylighter elements, and here the stability depends on the relative numbers ofprotons and neutrons.

We now consider the different types of radioactivity.

Types of radiation

Fig. 9.

You have probably seen the hazard warning sign for radio-active substances in a laboratory at school or college orin a hospital or factory. The danger lies in the fact thatour bodies cannot detect radi~tion from a nucleus eventhough it can penetrate our bodies and damage their cells.Here we consider three types of radiation which can beemitted by nuclei of radioactive isotopes (radioisotopes).


(13) describe the properties of alpha, beta and gamma radiation in terms ofcharge, mass and behaviour in a magnetic field;

(14) state the relative penetrating powers of alpha, beta and gamma radiation.

Read about the three types of radioactivity and their properties,listed in Objective 13, so that you can do the following exercises.Note that although the distinction between radiation and particlesis rather an arbitrary one, as you will see later, we usually regardy-radiation as an electromagnetic wave, and a and S emissions as particles.

o'If

17

Exercise 19 Fig. 10 shows how alpha and beta particles and gammarays, emitted from a radioactive source, S, behavein an electric field.(a) Use the information on the diagram to identify

the type of emission present at P, Q and R.(b) By what other means could a similar pattern of deflection

of the three types of radiation be caused?

Q

Fig.10. lead shield

(Answers on page 88.)

Exercise 20 Copy and complete the following table to summarisethe properties of alpha, beta and gamma emissions.

Table 3

Extent ofRelative deflection in Relativemass and electric or penetra-

Emission Nature charge Symbol magnetic field tion

alpha, exbeta, Bgamma, y


It is important for you to realise that the electrons in B-emission come fromthe nucleus. You consider this point in the next exercise.

A nucleus consists of protons and neutroni and yet,during beta decay, it gives off electrons. Usingisotopic symbols, write an equation to sho~ howthis is possible.(Answer on page 88)

Exercise 21

In the next section you apply your knowledge of alpha and beta particles towriting nuclear equations.

18

Nuclear reactionsWhereas chemical reactions leave the nucleus untouched and involve only theelectrons surrounding it, nuclear reactions rearrange the particles withinthe nucleus. Also, different elements may be formed, in a process known astransmutation, which does not, of course, occur in chemical reactions.

We now examine some nuclear reactions and show you how to write equations forthem.


(15) complete and balance simple nuclear equations.

The basic nuclear reactions are alpha and beta particle emission, often calleda and B decay. We go through the alpha decay in detail in the next workedexample. Read through it and then do the exerclse which follows.

Worked Example When thorium-228 decays, each atom emits one alphaparticle. Write a balanced nuclear equation toshow the process.

Solution1. Write out the equation, putting in letters for the unknowns:

2~~Th + ~He + ~ XIn these equations, the atomic numbers and mass numbers of each side mustbalance; this allows you tIT calculate the unknowns, A and Z and X.

2. Find the atomic number of the new element, X, using the atomic numbersshown in the equation.

9090Th

Z 90 - 2 = 88

3. Use a Periodic Table to identify the new element:element with atomic number 88 is radium

X = Ra4. Find the mass number of the particular isotope of radium, using the mass

numbers in the equation.228Th + 4He + AX

228 4 + A

• A 224

19

5. Write out the complete equation:

Note that ionic charges are not shown in nuclear equations. You maywonder, for example, why we do not write

In fact, the positive ions tend to pick up stray electrons and so thecharges are usually omitted as a simplification. This also focusesattention on changes in the nucleus.

Now try some calculations yourself, by doing the next exercise:

Exercise 22 Write balanced nuclear equations to show the alphadecay of:(a) 2~~PO,

(b) 2 ~ ~Rn.


You can adapt the method given in the last worked example to write an equationfor B decay.

You may need to remind yourself of how the process takes place (see youranswers to Exercises 20 and 21); then go on to try the next exercise.

Exercise 23 Write balanced nuclear equations to show the betadecay of:(a) 2~~PO,

(b) iiNa,

(c) l~~Ag.(Answe rs on page 88)

For further practice in writing nuclear equations, try the next exercise.

Exercise 24 Write the nuclear equations which represent:(a) the loss of an a-particle by radium-226,(b) the loss of a B-particle by potassium-43,(c) the loss of an a-particle by the product of (b) .(Answers on page 88 )

Finally, to summarise your knowledge of the effects of alpha and beta decayon the nucleus, do the next exercise.

20

What happens to the atomic number and the massnumber of a nucleus when it emits:(a) an a-particle,(b) as-particle.(Answer on page 88

Exercise 25

Before we go on to consider the rate at which radioisotopes decay, we spend ashort time considering nuclear stability. In other words, why do somenuclides decay and not others?

Nuclear Stability

Objective. When you have finished this section you should be able to:

(16) explain why certain nuclei are unstable, in terms of neutron/proton ratio.

Read about the stability of nuclei in your textbook. Look outfor a diagram like Fig. 11 and read the passage that accompaniesit.

oQJ

To test your understanding of why certain nuclei are unstable, work throughthe following exercise, using Fig. 11, which shows the number of protons andneutrons in all stable nuclei, as a guide.

140~----~~----~------~------~------~--

120~----~r-----~-------;-st-a~b~le---:~.-------+--isotoP~.i:~::

.~:!. 1/100~--t-:j----:-:-----t--.~: /--+--

~I 80~----~r-----~----~~------~~-----+--i j:i :.:.~./; 60~----~------~--~--~~-----+-------+--

~ .;.:.~r./ on : proton

;.~::. / ~~~~rof 1 : 140~----~~~--~~----~-------+-------+--

~

oFig. 11. Composition of stable nuclei

20 40 8060protons (Z)

21

100

Exercise 26 (a) From the graph, identify the heaviest knownstable nucleus, using isotopic symbols.

(b) Calculate the neutron to proton ratios (N/Z)for these stable nuclei:(i) the nucleus identified in (a)

(iii) l~C(c) Describe how the ratio N/Z for stable nuclei changes with

increasing atomic number.(d) By calculating N/Z ratios, predict whether the nuclei listed

below are liKely to be stable or unstable. ChecK yourprediction against the graph.

(i) 1~C

(ii) ~gZn

(iii) l~~Ag(Answers on page 88)

(iv) l~~Ba

To complete this section, try the following exercise.

Exercise 27 1~C is known to be a S emitter(a) Write a nuclear equation for the emission.(b) Work out the N/Z ratio for reactant and product

nuclei.(c) In view of the N/Z ratios, what can you conclude about the

stability of reactants and products? Summarise the wayB-emission changes the stability of a nucleus.


The decay of a single unstable nucleus is instantaneous and we cannot say whenit will happen. However, we can measure the rate of decomposition (decay) ofa sample containing many nuclei by counting the number of disintegrationswhich occur in unit time. In the next section, we look at the way in which therate of decay varies with time.

THE RATE OF DECAY OF RADIOISOTOPESThe rate at which a particular radioactive isotope decays depends only on theamount present - it is unaffected by external factors such as temperature orpressure. In this section, we introduce the idea of half-life. This providesboth a way to compare the rates of decay of different isotopes and, since notwo isotopes have exactly the same half-life, a method of identification.

Objective. When you have finished this section, you should be able to:

(17) define the term half-life.

22

Read about half-life in your text-book. The term is used inconnection with other reactions too, but you should concentrateon references to radioactive decay. We suggest you don't worryabout a mathematical treatment at this stage - look for agraphical description. This should be sufficient to help you dothe next two exercises.

Exercise 28 (a) Define the term 'half-life' as applied to aradioactive isotope.

(b) Why is it meaningless to speak of the 'total-life' of a radioactive isotope?


Exercise 29 (a) Use the following data to plot a decay curve forthe transuranium element, americium-239.

Table 4

Mass of sample/g time/hr

0.512 00.256 120.128 240.064 360.032 480.016 600.008 720.004 840.002 960.001 1880.0005 120

oGJ

Plot mass of sample on the vertical axis and time on thehorizontal axis.

(b) What happens to the rate of a radioactive decay reaction,like this one, as it proceeds?

(c) How long would it take for the mass of americium to reachzero?

(d) Describe the shape that the curve would have if we hadasked you to plot activity,in counts min-I, rather thanmass of sample.

(e) What percentage of the original activity remains afterten half-lives?


23

We now go on to consider an important application of the half-life of radio-isotopes, radioactive dating.

Radioactive datingHalf-lives of certain radioactive elements have been used to calculate the ageof rocks and estimate the age of the earth. In this section, we examine theuse of carbon-14 in the dating of archaeological remains.


(18) explain the use of the l~C isotope in radiocarbon dating.

Read about radiocarbon dating in your text-book. Find out why theamount of l~C in the atmosphere is constant and how archaeologistsuse this to find the age of objects from the past. We suggest thatyou do not concern yourself too much with the mathematical aspectsat this stage, but you should be able to do simple calculationsbased directly on the concept of half-life, as in the next exercise.

oill

Exercise 30 (a) Complete the following nuclear equation whichshows how carbon-14 is formed from nitrogen-14by the action of cosmic radiation:

liN + 6n + l~C + ~ X

(b) Carbon from a piece of wood from a beam found in an ancienttomb gave a reading of 7.5 counts per minute per gram.New wood gives a reading of 15 counts per minute per gram.Estimate the year in which the tomb was built given thatthe half-life of l~C is 5730 years.

(c) What is assumed to be constant over the period?(Answers on page 89)

So far, we have described only natural radioactivity. In the next sectionwe consider some of the nuclear reactions that have been carried outartificially.

ARTIFICIAL TRANSMUTATION OF ELEMENTSAll known elements heavier than uranium have been created artificially in thelast fifty years. They are known as the transuranides, as they come afteruranium in the Periodic Table. The most recently-discovered element, number104, is the first transactinide, as it follows actinium in the PeriodicTable but there are claims for the discoveries of elements 105 and 106. Inthis section, we look at various transmutation reactions.

24


(19) write nuclear equations for reactions in which an element is bombardedby a neutron, proton, alpha particle or small nucleus.

Transmutation reactions are usually achieved by bombarding an element with astream of particles. These may be neutrons, protons, alpha particles or smallnuclei such as boron or carbon.

For example, if uranium-238 is bombarded with neutrons, it forms a new andunstable isotope, uranium-239

in a reaction known as neutron capture. This unstable isotope then decomposesin two stages by beta decay. To see which new elements are formed, try thenext exercise.

Exercise 31 Uranium-239 decays in two stages, by emitting betaparticles. Write balanced nuclear equations to showwhich products are formed.(Answers on page 89)

The next exercise is about the formation of another transuranide, curium.

Exercise 32 Complete the following nuclear equation to find outwhich nuclide, if bombarded with alpha-particles,changes to Cm-242.

AX + ~HeZ

(Answer on page 90)

2~~Cm + 6n

Now try the next two exercises which give you more practice in identifying theunknowns in equations for nuclear bombardment reactions.

Exercise 33 Work out the values of Z and A, and identify thesymbols corresponding to X in the followingequations.(a) l~F + 6n A ~He-+ ZX +

(b) l~O + ~He -+ igNe + ~X

(c) l~N + AX -+ l~C + ~HeZ


2552-8

Exercise 34 Work out Z, A and X in the following equations:

~(a) 2~~U + liN -+ AX + 56nZ(b) 2~~Cm + ~X -+ ig~No + 86n

(c) 2~~Cf + 19B -+ ~x + 5~n


Bombardment can also cause the break-up of a nucleus into smaller fragments.Try working out what happens when neutrons bombard uranium-235.

2~~U + 6n -+

Exercise 35 Work out A, Z and X in the equation:

(Answer on page 90)

Fig. 12. Uranium fission reaction

oI

This reaction, where the nucleus breaks into two roughly equal fragments, iscalled a fission reaction. In the process, some of the mass is lost from theuranium nucleus and transformed into a great deal of energy, which is set free.

Reactions like this are the basis of the nuclear power industry but have alsobeen used for destructive purposes •••••••

Hiroshima, 1945

Fig. 13.

26

We have already mentioned one use of radioisotopes, in dating objects from thepast. In this final section on radiochemistry, we suggest some reading on themany other uses of radioisotopes.

Uses of radioisotopesObjective. When you have finished this section, you should be able to:

(20) state at least four ways in which radioisotopes are used and explainthe principle behind each use.

Most text-books have a section covering the uses of radioisotopes.Look through a few books until you find one that gives a fairlydetailed treatment. Among the uses to look out for are:

oW

atomic bombsnuclear reactorsradiotherapyradiocarbon datingtracer techniques in biology

and medicinethickness measurement

Fig. 14 Mobaltron cobalt unit

When you have read about the uses to which radioactive isotopesare being put, answer the following teacher-marked exercise:

Teacher-marked Exercises are designed to give you practice in essay-typequestions. Before you start one~ look back through your notes on the topicto make sure that you are clear about the main points. Next~ read over thequestion carefully. Then~ with all notes and text-books closed~ make a shortplan of your answer. Spend about half-an-hour writing and then hand yourfinished answer~ together with your plan~ to your teacher.

Teacher-markedExercise

Choose three ways in which radioisotopes are usedtoday. For each one, explain the underlyingprinciple.

27

LEVEL ONE CHECKLISTYou have now reached the end of Level One of this Unit. The following is asummary of the objectives in Level One. Read carefully through them and checkthat you have adequate notes.

At this stage you should be able to:

(1) calculate the density of an atomic nucleus, given the nuclear volume, VN;

(2) define the terms atomic number, Z and mass number, A;

(3) & (5) explain what isotopes are and use isotopic symbols to describe them;

(4) use values for atomic number and mass number to calculate the number ofprotons and/or neutrons in the nucleus;

(6) & (7) describe the principal parts of a mass spectrometer and explain howit works;

(8) identify peaks on a simple mass spectrum and use them to calculate therelative abundances and masses of ions;

(9) & (10) calculate the relative atomic mass of an element from (a) a massspectrum, (b) percentage abundance data;

(11) sketch a mass spectrum, given relevant data;

(12) calculate the mass defect of an atom, given appropriate masses in atomicmass units;

(13) & (14) describe the properties of alpha, beta and gamma radiation;

(15) complete and balance simple nuclear equations;

(16) explain why certain nuclei are unstable, in terms of neutron/proton ratio;

(17) define the term half-life;

(18) explain the use of the l~C isotope in radiocarbon dating;

(19) write a nuclear equation for a reaction in which an element is bombardedby a neutron, proton, alpha particle or small nucleus;

(20) state at least four ways in which radioisotopes are used and explain theprinciple behind each use.

LEVEL ONE TESTTo find out how well you have learned the material in Level One,try the test which follows. Read the notes below before starting.1. You should spend about 1 hour on this test.2. Hand your answers to your teacher for marking.

28

LEVEL ONE TESTQuestions 1 to 5 are either questions or incomplete statements followed byfive suggested answers. Select the best answer in each case.

Which of the following statements about isotopes is FALSE?A The presence of isotopes and their relative abundance in

a sample of an element may be determined by a massspectrometer.Isotopes ~f the same element have the same number of protons.Isotopes arise because different atoms of the same element havedifferent numbers of neutrons.The existence of isotopes is a cause of non-integral chemical relativeatomic masses of elements.

1 .

B

C

0

E

1002.

~0a.>occo\JC::J 50.0coa.>>.~~

Stable isotopes generally have more protons than neutrons. (1 )

, 'IFL. ... "'

.....,.T ;.... ! TT, .r .. , ..

,+. i·········· .1....,.+

, ,. , ......,.. ,.. ,.. , ..,,. , ,

, ,"

•

: .,

., "....

....,.... , .. i .. ,.. , ...

j.,

: .... .

" .1 :.: .....I

_I _I. .t I _I.

Fig. 15.

63 64 65 66 67 68 69 70 71mass number

The graph shows the relative abun-dances of four isotopes of a certainelement. Its relative atomic masswill be (to the nearest wholenumber)A 64B 65C 66

o 67E 6B

(1 )

o 24.30

3. The isotopic composition of a certain element X is Bo% 24X,10% 25X and 10% 26X. The relative atomic mass of X isA 25.00 B 24.67 C 24.33 E 24.25

Archaeologists can determine the age of organic matter bymeasuring the proportion of l~C present. Assuming thatcarbon-14 has a half-life of 5600 years, a piece of woodfound to contain l/e as much carbon-14 as living materialis calculated to have an age, in years, ofA 44 BOO B 16 BOO C 2 BOO 0 1 400 E 700

5. The NUCLEUS of fiNa containsA 23 protons and 11 electronsB 23 protons and 11 neutronsC 11 protons and 12 neutrons0 11 protons and 12 electronsE 12 neutrons and 11 electrons

4.

(1 )

(1 )

29

In questions 6 to 8 inclusive, one, more than one or none of the suggestedresponses may be correct. Answer as follows:A if only 1 , 2 and 3 are correctB if only 1 and 3 are correctC if only 2 and 4 are correct0 if only 4 is correctE if some other response, or combination, is correct.

6. In the nuclear reaction

~~Ca + X -+ ~~Sc + Y

the particles X and Y could be respectively1 • iH and e- 3. ~Li and ~He2. ~He and iH 4. ~Be and ~Li

7. In the natural state the element M consists of the isotopesi~M, i~M and f~M in the ratio 60:3:2 respectively. Correctstatements about M in its natural state include that1. the relative atomic mass is between 28.0 and 28.52. atoms of M each contain 14 electrons3. atoms of M may contain 14, 15 or 16 neutrons4. atoms of M each contain 14 protons.

8. The unstable nucleus 2~~Pb decays with B-particle emission,having a half-life of 10 hours. From this it follows thatthe1. mass number of the product is 212

2. atomic number of the product is 81

3. fraction of the original isotope remaining after 20 hours is ~4. nucleus formed is stable.

For questions 9 and 10, choose an answer from A to E as follows:A Both statements true: second explains firstB Both statements true: second does not explain firstC First true: second false0 First false: second true

E Both false

First statement Second statementg. Gaseous isotopes of a given

element, in ionic form, canbe separated by passing themthrough a magnetic field.

Each particular isotope of agiven element has the samenumber of protons and hencepositive charges on the nucleus.

30

(1 )

(1 )

(1 )

(1 )

10. The mass spectrometer CANNOTdetermine the relative mole-cular mass of organiccompounds.

The mass spectrometer measuresthe masses of ions, notmolecules.

(i) electron(ii) proton

(iii) neutron(iv) isotopes

11 . (a) Explain what is meant by each of the following terms:

(b) The atomic number provides three pieces of informationabout qn·element. What are they?

(c) The radioactive atom 2~ciRa decays by a-emission w~th a half-lifeof 3.64 days.(i) What is meant by 'half-life' of 3.64 days?(ii) Referring to the product of the decay, what will be itsmass number and its atomic number?

(3)

(iii) Radium is in Group II of the Periodic Table.will the decay product be?

(d) Explain briefly the principles underlying

In what Group(4)

(i) the use of radioactive isotopes as 'tracers' ~(ii) the dating of dead organic matter using radiocarbon, l~C. (6)

12. (a) Explain what you understan~ by the terms:(i) mass number (ii) relative atomic mass

(b) Calculate the relative atomic mass of copper assumingit to contain 70% of 63CU and 30% of 64CU.

(c) Briefly explain the pr-inciples of the use of the mass spectrometerfor determining the mass number. (6)

(d) Complete the following equations

(4)(e) The activity of a sample of 2~~Rn is reduced to 25% of its initial

value after eight days. What is the half-life of 2~~Rn? (2)

13. A mixture of ~H2 and ~;Br2 was analysed in a mass spectrometer.The following pattern of lines due to singly-charged ions wasobtained.

I I : I I =2 4 81 83 162

mass number onFig. 16. instrument scale

(a) state which ions give rise to each of these lines. (5)(b) What apparent mass number would register on the instrument scale

if the heaviest of these ions acquired a second charge? (1)

31

14. (a) Copy Table 5 and complete it by inserting properties ofthe three types of radioactivity.Table 5

Relative charge Relative mass

a

Sy (3)

(b) Which of the types of radioactive emission has the greatestpenetrating powerl and which has the least? (2)

(c) Among the lighter elementsl any isotope with a neutron/protonratio greater than one is likely to emit radiation to bring theratio closer to one.(i) Write an equation for the decay of sulphur-35 by emission ofa single particle.(ii) Write down the neutron/proton ratios for the reactant andproduct nuclides. (4)

(d) Sulphur-35 has a half life of 88 days. How long will it take fora sample to decay to(i) one quarter of its original activitYI(ii) zero activity? (2)

(Total 60 marks)

32

LEVEL TWO: ELECTRON ARRANGEMENTS

INTRODUCTIONHaving considered the nucleus in Level One, we now move on to the electrons.We cannot 'see' electrons in a physical sense and yet chemistry is based ona description of where they are in an atom and how they move. Informationabout the arrangement of electrons has been obtained by 'disturbing' them,in two important ways:

(a) by bombarding them with streams of fast-moving particles and sodetaching them from the atom;

(b) by forcing them into higher energy states and observing what happenswhen they return to normal.

Method (a) allows us to measure approxi~ately the energy required to detachan electron, called the ionization energy; method (b) is the basis ofemission spectroscopy and provides a better way of measuring ionizationenergies.

The study of ionization energies helps us to understand how electrons arearranged around the nucleus and how they behave in chemical reactions.

IONIZATION ENERGYIn your study of the mass spectrometer, you saw in Level One how atoms loseelectrons to become positively-charged ions. In this section we consider theenergy change needed to bring about the process.


(21) define first ionization energy;(22) describe how ionization energy is measured by electron bombardment;(23) calculate ionization energy from the results of electron bombardment

experiments.

Read the section on ionization energy in your text-book. Look indetail at the definition of first ionization energy, bearing inmind that it refers to atoms in the gaseous state. Skim the parton measuring ionization energy by electron bombardment, also calledthe electron impact method. This should prepare you for the nextexercise and the experiment which follows it.

33

Exercise 36 (a) Define first ionization energy.(b) Write an equation to show the first ionization

of sodium.(c) Use your data book to find a value for the first ionization

energy of sodium.(Answers on page 90)

If it is available~ you should now watch the ILPAC videotape'Ionization Energy'.

If the videotape is not available, re-read the section onmeasuring ionization energy by the electron impact methodin a text-book.

oW

The next activity is an experiment to measure the ionization energyof argon by the electron impact method. The method is neithersuitable for many elements nor very accurate but it does clarify theconcept of ionization energy. In practice~ the values quoted forionization energy in data books have been obtained by emissionspectroscopy~ a method we shall cover at the end of this unit.

Estimating the ionization energy of a noble gasEXPERIMENT 1

AimThe purpose of this experiment is toestimate the ionization energy ofargon by the electron impact method.

Introduction

Argon atoms can be ionized by bombarding them with high energy electro~2:+Ar(g) + e -+ Ar (g) + e + e

t t t

high energy electron bombarding electronelectron from Ar with less energy

34

The process is carried out in an argon-filled radio valve, called a thyratron,as shown in Fig. 17.

The valve anode is kept at a negative potentialto serve as a collector of positive ions. Notethat the term 'anode' is not really appropriatehere as an anode is normally positively charged.

The grid is kept positive to attract electronsemitted from the heated cathode.

The heater provides energy whiGh allows thecathode to give off electrons.

Fig. 17.

The experiment takes place in several stages which we now illustrate withdiagrams of the valve:

1. The cathode is heated (by passing a currentthrough the heater circuit) and emits electrons.These are attracted towards the positively-charged grid, increasing their speed and energy.Some electrons are collected by the grid, whilesome pass through holes and move towards theanode. Since the anode is negatively chargedrelative to the grid, it repels electrons whichturn back from it and return to the grid.

Fig. 18.

2. As the potential betwee~ the grid and the cathodeis increased by adjusting a variable resistor, theelectrons passing through the grid increase inenergy but still cannot reach the anode. Notethat the lengths of the straight arrows in Figs.18 and 19 indicate their relative speeds.

Fig. 19.

3. When the electrons have enough energy, theyknock other electrons off the argon atoms,forming positive argon ions. These argon ionsare then attracted to the negative anodewhere they pick up electrons from the cir-cuit and cause a current to flow. This isregistered by a milliammeter and marks thepotential at which ionization takes place.

Fig. 20.

key'

electrono argon atomEB argon ion

In brief then, the potential between the grid and the cathode is slowlyincreased until there is a rapid jump in the current shown by the milli-ammeter. This is the potential at which ionization takes place and we cancalculate ionization energy from it.

35

Requirementscircuit board with labelled sockets for valve and connecting leadsargon-filled valve, type 884power supplies

(a) 6.3 V (AC or DC) for the cathode heater(b) 3 V (DC) for the anode circuit(c) 25 V (DC) for the grid circuit

potential divider, 250 Q} these may be included in the circuit boardprotective resistor, 200 Qvoltmeter, 25 VI high resistancemicroammeterl 100 ~A (0.1 mA)12 connecting leads

Procedure1. Insert the valve and connect the 6.3 V supply to the sockets labelled

'cathode heater'. Switch on to allow the valve to warm up for a minuteor two.

2. Connect the voltmeter, microammeter and 3 V supply to the appropriatelabelled sockets. Make sure the valve anode is negative with respect tothe cathode, as shown in Fig. 21. (In most valve applications I the anodeis positive, as the name implies.)

3V- + ------'------1.---.1....---Fig. 21.

J.1.A

protective resistor

grid-------I--- ...•....---TI

cathode

3. Set the potential divider to give the mlnlmum accelerating potential;connect the 25 V supply and the protective resistor, as shown in Fig. 21.If you are not sure about these connections I check with your teacher.

4. Slowly increase the potential and watch the voltmeter. At the same timel

watch the microammeterl which should read zero until ionization occurs.5. As soon as the microammeter needle begins to move, note the voltmeter

reading and reduce the potential to zero.6. Repeat steps 4 and 5, this time looking for two additional indications of

ionization:(i) a sudden decrease in the voltmeter reading (due to the surge in the

grid current),(ii) a small purple glow in the valve (looking down from the top).

You may need to move the potential divider control a little further to seethese effectsl but always return it to zero as soon as possible to avoiddamage to the valve.)

36

CalculationOne mole of electronsl on moving through a potential difference of one volt,acquires 96.3 kJ of energy*. To calculate the ionization energy of argon,multiply your voltage by this factor.

1st ionization energy of argon v x 96.3 kJ mol-1 V-1---kJ mol-1

Note that if you compare the value you have just calculated with the data-bookvalue, you will probably find it is up to 20% higher. This can be explainedby the limitations of the experimental method. The experiment is designed togive you an idea of the meaning of ionization energy, rather"than to provide anaccurate method of determining it. We will consider the more accurate method,based on emission spectra, towards the end of the Unit.

*The derivation of this factor is quite simplel but not important here. Wehave covered it in Appendix 2 to this Unit, page 83.

Question1. If another microammeter were included in the circuit for this experiment,

between the grid and the protective resistor, it would show a currentflowing throughout the experiment, rising suddenly after ionization.(a) EXDlain why a current· flows before ionization.(b) Suggest one reason for the sudden increase after ionization.


Now try the following exercise to test your understanding of the electronimpact method.

Exercise 37 In an electron bombardment experiment, a series ofreadings of current and potential was obtained andplotted as shown in Fig. 22.

2.5

2.0

«::t.<,

C 1.5~:l(.)

Q)

"00c: 1.0(0

0.5

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Fig. 22.potentialN

37

(a) Use the graph to estimate a value for the potential atwhich ionization occurs. Use a ruler to extend the verticalpart of the curve until it crosses the horizontal axis.This is known as 'extrapolation'.

(b) Calculate the ionization energy to which this valuecorresponds.

(c) Using another valve, containing krypton, ionization occurredat 14.0 V. Calculate the corresponding ionization energy inkJ mol-1

•


Now that you know what the first ionization energy of an element is and how itcan be measured, we turn our attention to the removal of more electrons froman atom and consider successive ionization energies.

Successive ionization energiesIf you repeated the electron bombardment experiment with more robust apparatusand continued to increase the accelerating potential after the first ionizationhad occurred, there would be a further sudden increase in current. This wouldindicate the removal of a second electron. The energy change corresponding tothis potential could be worked out in the same way and would give the secondionization energy for argon.

Theoretically, the bombardment process could go on until all the electronswere removed but, in practice, successive ionization energies have beenobtained from spectroscopic measurements. We consider this method later in theUnit. In this section we concentrate on the definitions of successiveionization energies.


(24) write equations representing second, third and subsequent ionizationenergies of a given element.

The important point about ionization energies after the first one is that anelectron is removed from a positively charged ion each time. To make sure youunderstand this idea, try the next exercise.

Exercise 38 (a) Write equations to show the first, second andthird ionization energies of aluminium.

(b) Would you expect the values of these ionizationenergies to increase or decrease, in the order:1st, Zrid , 3rd?

(c) Explain your answer to (b).(Answers on page 90)

38

Now we go on to consider how successive ionization energies give informationabout the arrangement of electrons.

Ionization energies and the arrangement of electronsIn this section you use successive ionization energy values for a specificelement and find that they provide evidence for the arrangment of electronsaround the nucleus.


(25) deduce the electronic arrangement of an element from a graph of lOgloionization energy against number of electron removed;

(26) use a graph of successive ionization energy .against number of electronremoved to provide evidence for the existence of subshells.

In the next two exercises, you examine successive ionization energy data forcalcium and draw conclusions about its electron arrangement.

Exercise 39 (a) For the element calcium, plot lOglO (I.E.)against the number (one, two, three ...Jof the electron removed.

Table 6

Number of Ionization LoglOelectron Energy (I.E.J (I.E./kJ mol-I)removed /kJ mol-1

1 590 2.772 1145 3.063 4912 3.694 6474 3.815 8145 3.916 10496 4.027 12320 4.098 14207 4.159 18192 4.26

10 20385 4.3111 57048 4.7612 63333 4.8013 70052 4.8514 78792 4.9015 86367 4.9416 94000 4.9717 104900 5.0218 111600 5.0519 494790 5.6920 527759 5.72

39

(b) What information does this graph give about the electronconfiguration of the calcium atom?

(c) Why were you asked to plot 10glO (I.E.) and not justionization energy?

(d) Explain why the ionization energy increases when electronsare successively removed from a given shell.


This exercise fits the Bohr planetary model of the atom with which you arefamiliar. The large jumps in the value of the ionization energy indicateshells of different energies. You probably used a diagram like one of thoseshown in Fig. 23 to represent the structure of the calcium atom.

Q ie8e 8e 2eV // I I

Fig. 23.

However, we now take a closer look at the ionization energies of electrons ina given shell, and find that this picture is oversimplified. There isevidence for a structure within each shell. To find out what this is, go onto do the next exercise.

Exercise 40 (a) From the data given in Exercise 39, plot a graph ~of ionization energy (not 10glo(I.E.)) againstthe number of electrons removed for electrons 3 ~~to 10.

(Let 1 cm = 1000 kJ mol-1 on the vertical axisand 1 cm = 1 electron removed on the horizontal axis.)

(b) In the previous exercise, you learned that large jumps inionization energy represent electrons being removed fromdifferent energy shells. What is your conclusion aboutthe small jump which occurs between the eighth and ninthelectrons?

(c) In view of your answer to (b), suggest how electrons arearranged in the second shell.


This exercise has shown you the shortcomings of the Bohr planetary model ofthe atom. But does this mean that the Bohr model is completely useless? Wenow pause to consider models in general before going on to a more sophisticatedpicture of the atom in the next section.

40

Models and their usefulnessYou are probably more familiar with the term 'model' to describe a scaled-downversion of an everyday object, such as a model car. But model cars differenormously in the accuracy and detail with which the original is reproduced.At one extreme is the miniature replica, identical in every feature,including an engine, which burns fuel and moves the car along. Less refinedis the familiar 'Dinky toy' model, which is recognisable in many details as aparticular make of car, but has no working parts. EVen less refined is thesort of model an architect might use for a new town centre plan - a solid, car-shaped block, to give an impression of the relative sizes of road and car.Finally, at the other extreme, there is the model a motorist.would use aftera car accident - just a rectangle on a map to indicate where the vehicle wasat the time of impact.

None of these models is strictly 'correct' but each has its own use in a givensituation. In a similar way, there are several models of the atom - from thesolid sphere of John Dal ton to the planetary model of Rutherford and Bohr wi thelectrons as particles circling a central nucleus in fixed orbits.

(a) The solar systemFig. 24.

(b) Planetary model of the atom

A further model, the orbital model, which we are going to use in the rest ofthis Unit, treats electrons as waves.

As we move more deeply into the subject, we meet increasingly detailed andsophisticated descriptions of atomic structure. But must we thereforediscard earlier descriptions as 'wrong' and useless? In fact, there is noneed to do so. For many purposes, such as explaining the states of matter,there is no point in using anything more complicated than the simple'billiard ball' picture; in other cases, the planetary model is all that isneeded. At A-level, you will continue to use the simple electron shell model,for example, to explain ionic compound formation.

Scientific theories are rather like models: they can be simple or elaborate,depending on the job they have to do. It is usually more sensible to ask, notwhether a model is 'right' but whether it is useful. This is an importantunderlying theme in chemistry (and in science generally) and we shall returnto it from time to time.

Before considering the orbital model of the atom as such, we spend a shorttime on the nature of electrons.

41

Wave-particle dualityUntil now, it has been convenient to think of electrons as minute, almost mass-less particles, but there is evidence to suggest that they also behave aswa\/es.


(27) describe briefly what is meant by the wave-particle duality of anelectron.

Electron beams can behave like beams of light. For example, they can bediffracted, and diffraction is a property of waves. Read about theevidence which shows that electrons can behave as waves. Try 'electrondiffraction' or 'electron, wave nature' in the index.

oGJ

Fig. 25(a) shows an electron diffraction pattern obtained by passing a beam ofelectrons through aluminium foil. Notice the similarity to Fig. 25(b) whichis the pattern obtained by passing X-rays through aluminium foil.

(a) (b)

Fig. 25. Diffraction patterns for aluminium produced by electrons (left) and X-rays (right)

Clearly then, we need more than one model for the electron. To explain someproperties, we regard electrons as particles; to explain others we regardthem as waves. In other words, they appear to have a dual nature. Thisphenomenon is known as 'wave-particle duality'.

It was by treating electrons as waves and applying to them mathematical methods,known as wave mechanics, that scientists came up with pictures of electrondistribution. We go on to consider this model, where electrons do not occupyfixed orbits as in the planetary model, but orbitals, which describe how theircharges are spread out in small regions of space.

42

THE ORBITAL MODEL OF THE ATOMThe main distinction between the planetary and orbital models of the atom isthat, while the planetary model assumes that electrons keep to fixed orbitsaround the nucleus, the orbital model is based on the probability of findingan electron in a certain volume of space.


(28) give a simple, non-mathematical description of an orbital in terms ofprobabilities;

(29) draw the shapes of an s-orbital and a p-orbital;(30) state the maximum number of electrons that an orbital can hold.

Look up 'orbitals' in a text-book and read the section on atomicorbitals. At this stage, ignore references to other sorts oforbital, such as molecular, metallic, bonding and anti-bondingorbitals. You need not worry about a mathematical treatment oforbitals.

oW

An important point to bear in mind as you do your reading is the closerelationship between the energy of an electron and its distance from thenucleus. As you saw from the successive ionization energy data, the furtheran electron is from the nucleus, the less energy is needed to strip it awayfrom the atom. Outer electrons are at higher energy levels, less stronglyattracted by the charge on the nucleus and, therefore, easier to remove.

In your reading, you may also come across the phrase 'quantum shell' used forenergy shell. It arises from the Quantum Theory which, when applied toelectrons in atoms, says that the electron can only exist in certain definiteenergy states. These energy states are called quantum shells.

OrbitalsAs an extra help in picturing an orbital, we now include a short analogy. Readthrough this before attempting the exercise which follows.

Imagine that you were able to take a large number of photographs of a hydrogenatom (which you are not), containing one electron. By superimposing thesephotographs, you would obtain an impression of where the electron spends mostof its time. The picture you would get would be something like Fig. 26 .

. '. -.

):!,~'J:.~U'.Fig. 26 Hydrogen atom 'charge cloud'

43

The picture is itself an over-simplification since it is restricted to twodimensions. The complete model is three-dimensional and spherical. Since eventhe two-dimensional picture is tedious to draw, we often use instead a boundaryround the region where the probability of finding an electron is high - about98% - as shown in Fig. 27. The space enclosed by this boundary is often calleda probability envelope, or an orbital. At a more advanced level, you may haveto make a mathematical distinction between probability envelopes and orbitals,but we shall regard them as the same, in common with most A-level text-books.

Fig, 27 Orbital boundary superimposed on charge cloud

Exercise 41 In the planetary model of the atom, we say that the ~electron has a definite energy and a definite positionin space. How does the orbital model differ from this? ~~(Answer on page 92)

How many electrons per orbital?In case you did not answer this question in your reading, we suggest you workit out for yourself, by doing the next exercise.

Exercise 42 The number of orbitals in a quantum shell is given byn2, where n is the number of the shell. Use yourknowledge of the total number of electrons in a shellto work out how many electrons a single orbital canhold.(Answer on page 92)

Not all orbitals are spherical like the one shown in Fig. 27. In the nextsection, we look at some other shapes as well.

The shapes of orbitalsThere are four types of orbitals whose shapes have been worked out, using wavemechanics. They are referred to by letter: s, p, d and f. These are theinitial letters of the words 'sharp', 'principal', ,diffuse' and 'fundamental',originating from work carried out on the hydrogen spectrum which led to ourpresent-day view of shells and sub-shells. You need only remember the initialletter.

You should be familiar with the shapes of sand p orbitals and we include dorbitals for interest, but f orbitals are too complex to show on a two-dimensional page.

44

s-orbitals o..

. o1s2s

z z z

p-orbitals x

y

pz py px

z z

y

x x

d-orbitalsz z z

y

x x x

Fig. 28. The shape of s. p, and d orbitals

Study Fig. 28 which shows the shapes of s, p and d orbitals as predicted bywave mechanical calculations. You should also return to the section onorbitals in your text-book and read descriptions of these shapes. Then dothe next two exercises.

Exercise 43 Explain why p-orbitals are labelled 'PX'I 'Py' and'pz'. (d-orbitals are also given labelsl but asthey are not straightforward we have omitted them.)(Answer on page 92)

Exercise 44 (a) How many electrons can be held in(i) an s-orbital,(ii) a set of three p-orbitals?

(b) Use one word in each case to describe the shape of(i) an s-orbitall

(Answers on page 92)(ii) a p-orbital.

45

In the next section, we go on to consider how many orbitals of each type thereare in each electron shell.

The number and type of orbitals in an electron shellEach shell has a certain number of orbitals associated with it. In thissection, we list these and you calculate the total number of electrons in ashell.


(31) state which orbitals are present in the first four electron shells;(32) write down the order in which orbitals are filled in the first four

electron shells.

The maximum number of electrons a shell can contain is given by 2n2, where nis the number of the shell. Use this expression in the exercise which followsto work out the total number of electrons in a shell.

Exercise 45 Table 7 giv8s the orbitals associated with the first.four electron shells. Copy the table and fill in thelast two columns to check the sum of the electrons inthe separate orbitals against the total in each shell.

Table 7

Number and Maximum number of Maximum number oftype of electrons in each electrons in the

Shell orbitals set of orbitals shell

First shell one s

Second shell one sthree p

Third shell one sthree pfive d

Fourth shell one sthree pfive dseven f


46

In the next section~ we go on to consider the order in which orbitals arefilled. First~ you need to know something about their different energy levels.Fig. 29 shows the orbitals in the first four shells for a typical light element~as well as some orbitals from the fifth to seventh shells. Each orbital isrepresented by a square box~ O. The vertical axis represents energy and isroughly to scale. Note~ however~ that the energies vary from element toelement~ and even the order of energy levels may be different for heavierelements (see ILPAC Unit IS: Transition Elements).o

Study Fig. 29 and then do the exercise which follows.

increasingenergy

Fig. 29.

s p f

6d1 I I I I I I I I5fi I I I I7s{ ] 6P-DTI 5d:j I I I I I I I I4f1 I I I I6s-D5P-DTI 4d1 I I I I I5s-D4p-[[JJ 3d1 I I I I I4sU3P-DTI

3s-D

2P-DTI2s-O

f-1S-O

Use Fig. 29 to list the first ten sub-shells in orderof increasing energy.(Answer on page 92)

Exercise 46

47

In an atom, the orbitals are filled in order of increasing energy, startingfrom 18. An aid to remembering this order is to write down the orbitals incolumns, as shown below.

78 7p 6d

68 6p 5d 5f58 5p 4d 4f48 4p 3d

38 3p

28 2p

18The order is then given by drawing diagonal lines through the symbols, as inFig. 30.

Fig. 30

You are now ready to study the way in which electrons fill the availableorbitals in an atom.

The arrangement of electrons in orbitalsWe shall start with hydrogen, the simplest element, which has a singleelectron in the lowest energy orbital, the is. Then we go through theelements in order of increasing atomic number, imagining the addition ofan extra electron each time.

48

This process is known as the aufbau*, or 'building-up' principle. As you gothrough it, the pattern of the Periodic Table emerges and we draw this togetherat the end of the section. We also introduce the conventional ways of writingout electronic configurations.

*Aufbau is a German word meaning to build up, pronounced 'owf-bow' (as in 'bow-wow' ).


(33) use the aufbau principle to work out the order in which orbitals arefilled in a given element;

(34) express electronic configurations using(a) the electrons-in-boxes method;(b) B, p, d, f notation.

(35) write down the electronic configuration of any element or ion in thefirst four periods of the Periodic Table.

The aufbau principleWe now state three important rules which determine the order in which electronsoccupy the vacant orbitals in an atom.

1. Of the available orbitals, the added electron will always occupy the onewith the lowest energy.

2. Each orbital may hold only two electrons, and they must have oppositespin*. (Pauli exclusion principle.)

3. Where a number of orbitals of equal energy are available, the addedelectron will go into an empty orbital, keeping electron spins the same,before spin-pairing occurs. (Hund's rule.)

*Electrons can be thought of as spinning on an axis like the earth. Unlikethe earth, however, which spins in only one direction, an electron can spinin either of two directions. The t represents one direction of spin; the +arrow the other. Furthermore, in anyone 'box' when there are two electronsoccupying it, they will spin in opposite directions. This is called spin-pairing and is shown as OCOAs an example of how Hund's rule operates, consider two electrons entering thep-orbital. There seem to be three possible arrangements.

Px Py Pz

I tit I IPx Py Pz

I t I + I IPx Py Pz

I t + I I I

but the first is the only one which conforms to Hund's rule.

49

As an analogY6 think of a double-decker bus in which passengers fill up thelower deck before climbing upstairs and in which6 given the choice, passengersprefer to sit alone rather than share the seats.

We now apply the rules and work through the elements from hydrogen accordingto the aufbau principle.

Hydrogen. The hydrogen atom contains one electron which therefore occupiesthe lowest energy orbital - the 18 orbital. The electron configuration isrepresented by:

15

OJHelium. The helium atom contains two electrons. Since the 18 orbital stillhas room for another electron, the second electron goes into it, and theconfiguration is:

15

[illLithium. The lithium atom contains two 18 electrons and the third electrongoes into the next orbital, i.e. the 28 orbital. Hence the electron configu-ration is:

25

[]15

[illNotice that we always label the boxes. By now you should be able to work outwhat happens for the next four elements.

Exercise 47 Draw the electron configuration of beryllium.(Answer on page 92)

OJ]2p

Exercise 48 Make three copies of part of Fig. 29as shown, and draw in arrows to showthe electron configurations of:(a) boron,(b) carbon,(c) nitrogen.(Answers on page 92)

o35

o25

o15

You can save time and space in writing down electron configurations by placingthe orbital boxes in a row, as we now show.

50

Boxes-in-a-rowObviously, on paper it is difficult to get the vertical spacings betweeDenergy levels right. However, the spacings are usually not critical and theboxes are most often placed side by side. We shall refer to this arrangementas 'boxes-in-a-row', or 'electrons-in-boxes'.

15hydrogen [[]

15helium [ill

15 25lithium [ill [[]

15 25beryllium [ill [ill

15 25 2pboron [ill OJ] I t I I

Remembering to label the boxes, do the next exercise:

Exercise 49 Draw boxes-in-a-row to show the electron configu-rations of (a) carbon, and (b) nitrogen.(Answers on page 92)

Now we look at a further simplification in writing down electron configura-tions.

Using a noble gas 'core'The 'boxes-in-a-row' method can become tedious, particularly if the atomcontains very many electrons. In any case, we are most often concerned withthe outermost electrons in an atom - the inner 'core' is not involved inchemical reactions. Consequently, we can use a symbol for a noble gas toreplace some of the arrows. This is possible for both the next two elements.Notice also that from this point on, electrons entering 2p orbitals have topair up with electrons which are already there. The electron configurationsare therefore:

25oxygen (He) [ill 2p

I til tit Iand

fluorine25

(He) [ill 2P

Itilt.lt I

51

Now try this shorter method for the first two elements in the next period.

Exercise 50 Using boxes-in-a-row1 and noble gas coresl draw diagrams ~to show the electron configurations of (a) sodium and(b) magnesium. ~~\(Answers on page 92 )

Another method of writing electron configurations does away with boxesaltogether.

In this methodl the electron configuration of hydrogen is represented by -

one electron in this orbital~ '--v-----'

1S1~

Using this notationl the next three elements in the third period are:

silicon1S22s22p63s23pl1S22s22p63s23p21S22s22p63s23p3

aluminium

phosphorus

andl of coursel the noble gas core can be used here too:

silicon(Ne)3s23pl

(Ne)3s23p2(Ne)3s23p3

aluminium

phosphorus

Now do the next exercise in which you use this notation for the last threeelements in this period.

Exercise 51 Use the sIp1d1f notation to write the electron configu-ration for(a) sulphur,( b ) ch l0 rine ,(c) argon.(Answers on page 92)

52

The electronic configurations of ions derived from atoms can be represented ina similar manner. Here are three examples.

15 25

rLi [ill OJ+ le" 15

"'---Li+ [ill

15

[ill25

[ill25

[ill

2PIt+lt+lt I

15

[ill2p

It.lt+lt.1

;--N+3e-

"'-N3- (He)2s22p6

The next exercise gives you practice at writing electron configurations of ions.

Exercise 52 Ca) Using the 8~ p~ d~ f notation~ write the electron ~configuration of(i) the oxide ion~ 02-~ ~~( ) M 2+ii the magnesium ion~ g •

(b) Which element in the Periodic Table has the sameelectron configuration as these two ions?


In the fourth period, the pattern becomes more interesting. This is sometimesknown as the first long period and we shall now see why. The electronconfigurations of the first two elements are straightforward. Work these outyourself, by doing the next exercise.

Exercise 53 Write the electron configurations of (a) the potassiumatom and (b) the calcium atom~ using the 86 P6 d6 fnotation.(Answers on page 93 J

53

Before you do the next exercise, look at the energy level diagram, Fig. 29.What does this tell you about the added electron in the next element,scandium?

Remember that an electron will always enter the orbital of lowest energy.Which has the lower energy - 3d or 48?

Also, you write out the orbitals in numerical order, not the order in whichthey are filled. Thus, the order from the third shell is:

38 3p 3d 48 4p 4d 4f 58 ..... etc.

Exercise 54 Write the electron configuration of scandium usingthe s,p,d,f notation.(Answers on page 93 J

Scandium, therefore, differs fr-om calcium by having one electron in the 3dorbital. Now, there are five equivalent 3d orbitals. Consequently, not justthe scandium electron, but ten electrons can enter the third shell before itbecomes necessary for them to go into the 4p orbital.

The series of elements:Sc Ti V Cr Mn Fe Co Ni Cu Zn

represents this filling-up of the d orbitals. (We will return to this in theILPAC Unit 'Transition Elements'.J

For an introduction to the electron configuration of this series of elements,try the next exercise:

Exercise 55 Write the electron configurations of(a) the titanium atom,(b) the vanadium atom,(c) the iron atom.In each case use

(i) electrons-in-boxes,(ii) the 8,p,d,f notation.

(Answers on page 93 J

After zinc, electrons enter the 4p orbitals until, at krypton, these are full.To see how electrons fill in the rest of the fourth period, try the nextexercise.

54

(a) +the gallium ion~ Ga ~Exercise 56 Write the electron configurations of

(b) the arsenic atom~(c) the bromide ion.In each case use

(i) electrons-in-boxes~(ii) the 8~ p~ d~ f notation.


The fifth period starts with rubidium and strontium~ very much like thefourth period. Then~ with the 58 orbital full~ electrons enter the 4dorbitals until these too are full. Finally. the 5p orbitals are filled.

In the next period~ the pattern changes slightly. Look again at the energydiagram~ Fig. 29. Use the information in the diagram to help you do the nextexercise.

Exercise 57 Write down the orbitals which are filled in goingacross the sixth period.(Answer on page 93)

The seventh period of the Periodic Table is similar~ but incomplete.

You can now look at the Periodic Table as a whole and explain the majorblocks into which it is divided. The Periodic Table shown in Fig. 31 isthe Ilong forml - to see why~ compare it with other versions of the table.Study the table and use it to do the exercise which follows.

s-block~

I II

p-block

III IV V VI VII 0-e-

Li Be B C N 0 F Ne3 4 5 6 7 8 9 10

r- r--d-block AI Si P S CI ArNa Mg t J.

11 12 r 13 14 15 16 17 18

K Ca Se Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Rb Sr Y f-block Zr Nb Mo Te Ru Rh Pd Ag Cd In Sn Sb Te I Xe.A37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg TI Pb Bi Po At Rn55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

Fr Ra Ae Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Ku87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104

Fig. 31.

55

(b) For the s- and p-block elements, the number ofthe last sub-shell to be occupied is the sameas that of the period. Is this true of the d- and f-blockelements? Give examples from Periods 4, 5 and 6.

Exercise 58 (a) Explain why the s-block, p-block, d-block andf-block are so called.


In the next section, we return briefly to the topic of ionization energy.

USING IONIZATION ENERGY VALUES TO IDENTIFY AN ELEMENTAt the start of Level Two we used ionization energies as evidence for theshells and sub-shells in a calcium atom. You should also be able to reversethis process to identify an element from its ionization energy values.


(36) identify an element, given values of successive ionization energies.

The following exercise is part of an A-level question. Work through it tomake sure that you can identify an element given 10glo ionization energy.

Table 8

Exercise 59 Here are the logarithms of all the successive ioniza-tion energies for a given element, X.

Electron number I 2 3 4 5 6 7 8

10glo (I.E.) 3.12 3.53 3.72 3.88 4.04 4.12 4.85 4.92

(a) Plot 10g1o (I.E.) against the number (first, second, third,etc.) of the electron removed.

(b) Write down the electronic configuration of this elementusing the s,p,d,f notation.

(c) To which group of the Periodic Table does the elementbelong?

(d) What is the formula of its ion?(Answers on page 93)

You should also be able to identify an element by inspecting the successiveionization energy values and identifying the major 'jumps' or increases aschanges of shell. The next exercise, which is part of an A-level question,gives you practice at this.

56

Exercise 60 The following table shows the first six ionizationenergy values for each of four consecutive elementsin the Periodic Table.

Table 9

Ionization energy/kJ mol-1

Element First Second Third Fourth Fifth Sixth

W 1260 2300 3800 5200 6500 9300X 1520 2700 3900 5800 7200 8800Y 420 3100 4400 5900 800[) 9600Z 590 1100 4900 6500 8100 10500

Which of the elements do you think(a) is a noble gas"(b) will form an ion with a single positive charge"(c) will form an ion with a double positive charge?(Answers on page 93 )

At the end of the last section" you saw how the addition of one electron toeach successive element gives rise to the Periodic Table. We now consider thepattern which emerges from the first ionization energies of successive elements.

First ionization energies of successive elementsIf the first ionization energies of successive elements in the Periodic Tableare plotted against atomic number, an interesting graph emerges.


(37) plot a graph of first ionization energy against atomic number;(38) explain the term 'periodic' with reference to the plot of first

ionization energy against atomic number;(39) explain the changes in first ionization energy that take place across

the second period.

Exercise 61 Plot a graph of first ionization energy againstatomic number for the first twenty elements (i.e.up to Ce ) ,

Label the vertical axis: '1st ionization energy/kJ mol-1"

and extend the scale from zero to 2500 (in intervals, say,of 500).Label the horizontal axis: 'Atomic number' and extend the scalefrom zero to 20.

Obtain the necessary ionization energies from your data book.Label each point with the symbol for the element and join eachpoint to the next by a straight line.(Answer on page 94)

57S2-C

Your graph should clearly show a pattern for the elements of the second period(Li to Ne) which is repeated for those of the third period (Na to Ar).

There is a general increase along a period with discontinuities between Be(Z=4) and B (Z=5) and between N (Z=7) and 0 (Z=8) in Period 20 There arealso discontinuities for the corresponding elements in Period 3.

Use your text-book to read about the changes in first ionization ~energy across a period. Look for an explanation in·terms of: ~1. the extent to which inner-shell electrons 'shield' the outer-shell ~

electrons from attraction by the nucleusj2. the difference in energy between sand p orbitals;3. the difference between removing a paired electron and an unpaired

electron;Note that the so-called stability of half-filled orbitals is not, in itself,an explanation - it is part of the pattern which needs explaining!

Before you do the next exercise, look at Fig. 32. You will recognise that the-first part of this graph corresponds to the one that you have drawn in Exercise61. You wi!l also see that the repeating pattern appears at higher atomicnumbers: first ionization, energy is a periodic property of the elements.

2000

'I(5EJ.s:

~ 15000)t-O)C0)

C0.~ 1000co(/)

'c.Q+-'CJ)t-

'+=500

He

Ne

I Ar

f JKr

j

IXe!

J Rn,

N J / ~ ~

! \(V! II jy ~,f~~Li Na ~

•K Rb Cs

10 20 30 40 50 60 70 80 90atomic number

Fig. 32.

58

Now use Fig. 32 in order to do the next exercise.

(a) between hydrogen and helium,(b) between helium and lithium,(c) between beryllium and boron,(d) between nitrogen and oxygen.(e) along the peaks. Fig. 32 (for the noble gases),(f) along the lowest points (for the alkali metals) .

Exercise 62 Explain the changes in first ionization energy

(Answer on page 94)

At the beginning of Level Two, we mentioned two ways of disturbing an atom inorder to find out about its electronic structure. We then dealt with thefirst of these - electron bombardment - and now we come to the second -emission spectroscopy.

EMISSION SPECTROSCOPYYou know that white light consists of a continuous range of wavelengths whichwe distinguish by colour. Fig. 33 shows a typical arrangement for producinga spectrum. Each line is an image of the slit caused by a particular wave-length of light. If there is a continuous range of wavelengths, the linesmerge together into bands of colour in a continuous spectrum.

screen

light from _a ray box

Fig. 33

Coloured light emitted from sources such as sodium street lamps, neon lightsand coloured flames. generally consists of a mixture of a limited number ofwavelengths. Emission spectroscopy is concerned with the examination of thissort of emitted radiation.


(40) describe the difference between a continuous spectrum and a lineemission spectrum.

We start this section with an experiment in which you see some commonemission spectra for yourself.

59

EXPERIMENT 2Using a hand spectroscope to observe theemission spectra of some s-block elements

AimThis experiment is designed to give you aqualitative introduction to the spectra emittedby some s-block elements when their atoms areexcited by heating samples in a Bunsen flame.

IntroductionYou use a hand spectroscope to observe the continuous spectrum emitted by thetungsten filament of a light bulb. Using aflame test wire, you then obtaincoloured emissions from some s-block elements, view these in turn through thespectroscope and compare them with the continuous spectrum from the tungstenfilament.

We recommend that you work in pairs in this experiment. All three operations- preparing the flame test wire, obtaining a brightly-coloured flame andhaving the spectroscope ready to look at the flame for the few moments thatit lasts - are fairly tricky and require practice and concentration. Wesuggest that one person prepares the flame while the other stands ready withthe spectroscope. You can then change roles so that you both have a chanceto observe each spectrum.

Requirementsfume cupboard with gentle fanelectric lamp with tungsten filament pearl light bulbhand spectroscopecolour plate of spectraBunsen burner and bench protection sheetflame test wire (or tongs and supply of filter paper) I~Ihydrochloric acid, HCI, concentrated ----------------------boiling tube or other glass container for hydrochloric acidsmall pestle and mortarspatulaswatch glassesat least three of the following:

barium chloride, BaC12(s)calcium chloride, CaCI2(s)lithium chloride, LiCI(s)potassium chloride, KCI[s]sodium chloride, NaCI(s)strontium chloride, SrCI2[s)

60

Spectroscope. UNDER NO CIRCUMSTANCES must you look through thisat the sun. If you do so, your eyes may be permanently damaged.

Hazard warnings

Hydrochloric acid has a vapour which irritates and can damagey6ur eyes. Wear safety spectacles and work in the fumecupboard for this experiment.

Procedure

1. Switch on the lamp and look at the bulb through the spectroscope. Lookfor a series of colours, one running into the next. This is a continuousspectrum. Compare what you see with the coloured plate showing theemission spectrum from a tungsten filament.

2. Hold the spectroscope up to a window which does not face the sun.You must NEVER point the spectroscope pirectly at the sun. Thiscould result in permanent damage to your eyes.You should see the continuous spectrum of visible light.Light the Bunsen burner - adjust it to get a roaring flame.3.

4. Dip the flame test wire into concentrated hydrochloric acid, then I~Ihold it in the hottest part of the flame. Repeat the processuntil there is little or no colour from the flame test wire inthe flame. You may have to repeat this step several times,especially towards the end of the experiment, but certainly no more thantwelve times.

5. Crush a little of the salt to be tested finely in a pestle and mortar andmix with a little concentrated hydrochloric acid on a watch glass. Becareful here - use just enough of the acid to give you a semi-solid'mush' of crystals.Dip the cleaned flame test wire into the mush of the salt to be tested.Adjust the flame until it is pale blue and hold the wire in it. Yourpartner should be standing by with the spectroscope and should now lookthrough it at the flame. Look for brightly coloured lines.There are several lines for each element and it will probably not bepossible to get them all into view at once. The yellow line in the sodiumspectrum is easy to see and will probably persist through the spectra ofall the elements you try. You can use this line to help you locate lineson the spectra of the other elements, by looking either to the right orleft of it. Checking with the coloured plate of spectra will give you anidea of where to look for lines from a particular element.

7. Repeat steps 2-5 with the salts of at least two other elements. Also usethe spectroscope on any other vapour lamps which may be available,including street lamps, if there is one in view from the laboratory.

6.

61

Question

What is the difference between a continuous spectrum and a line emissionspectrum?(Answer on page 94)

Now that you have examined some spectra, we go on to explain why the colouredbands are produced.

Why do atoms emit light?In this section, we consider what is happening when atoms give out light.This phenomenon is the basis of emission spectroscopy.


(41) explain the emission of light by atoms in terms of excited states;(42) state the relationship between wavelength and frequency;(43) state the relationship between energy and frequency of radiation

(Planck's relationship).

The process that takes place when atoms of an element are given energy - byheating them in .aBunsen flame, for example, or by passing an electricdischarge through a gas at low pressure - is summarised in Fig. 34.

>-E>Q)cQ)

Fig. 34.

atom returnsto groundstate

atom in 'excited' state

o1

energy Iabsorbed I

IIIII

t'\./\./'- hv energy givenout as light

atom ingroundstate

At room temperature, nearly all the atoms in a given sample of substance arein the ground state, i.e. the electrons occupy the orbitals of lowest energy.

In a flame, or other energy source, electrons move to orbitals of higherenergy. The resulting excited states are not stable: each excited electronsoon falls to a lower energy state and, in the change, a definite amount ofenergy, called a quantum, leaves each atom. The energy appears as radiation ofa particular wavelength, which may be visible and coloured. The emissionspectra you have been looking at consist of a series of coloured lines, eachline corresponding to a particular energy drop, from a higher energy level toa lower one. The greater the number of electrons making a particular transition,the more intense the corresponding spectral line.

62

When you looked at ordinary daylight through a spectroscope, however, you sawa continuous spectrum. In other words, a beam of white light consists of amixture of coloured beams. The different colours correspond to differentvalues of wavelength, A (Greek letter lambda). Fig. 35 indicates the approxi-mate wavelength boundaries and the complete span (400 nm - 700 nm) is calledthe visible range.

wavelengthInm

400 500 600 700 800ultra-violet-violet-indigo- blue-green -yellow-orange ---- red---infra-red

frequencyIs-1Fig.35. Visible spectrum

Coloured beams can also be distinguished by their different frequencies.Frequency is represented by the symbol v (Greek letter nu, pronounced 'new').study the diagram of the spectrum and use it to answer the followingexercise:

Exercise 63 USing the information in Fig. 35, write the relation-ship between wavelength and frequencyLa) in words,(b) as a mathematical statement.(Answers on page 94 )

The proportionality constant is the speed of light, c, so the equationlinking wavelength and frequency is:

A = ~ where c is the speed of light (2.998 x 108 m S-l)V

All radiation is a form of energy~ which can only be transmitted in discrete'packets' called quanta. The energy of each quantum is proportional to thefrequency of the radiation. Fig. 36 shows the complete electromagneticspectrum (of which Fig. 35 represents just the central part)D Study it for afew moments and then do the next exerciseo

visible

spectrum microwave infra-red ultra-violet X-rays

wavelength /nm 108 107 106 105 104 103 102 101 10-1

frequency/s-l 3xl09 3 x 1010 3 x 1011 3 x 1012 3 x 1013 3 x 1014 3 x 1015 3 x 1016 3 x 1017 3 x 1018

enerqv/k.J mol' 1.2 x 10-3 1.2 x 10-2 1.2 x 10-1 1.2 1.2 x 10 1.2 x 102 1.2 x 103 1.2 x 104 1.2 x 105 1.2 x 106

Fig.36 Complete electromagneticspectrum63

Exercise 64 Explain why ultraviolet rays are more harmful to ourskin than infra-red rays.(Answer on page 94 )

The relationship between a quantum of energy and the frequency is:

E hv

where h Planck's constant and V = frequency of radiation.

This important relationshipl often called Planck's relationshipl has providedthe key to finding out the differences between energy levels in atomsl as weshall see in the next section.

The visible part of the hydrogen emission spectrumIn this section, we examine the visible part of the hydrogen spectrum indetail and relate the energy of light emitted to the electron transitionstaking place in the atom.


(44) calculate the frequency of a given form of radiation using therelationship A = C/Vi

(45) calculate the energy associated with a given form of radiation usingPlanck's relationshipi

(46) explain how the energy of a line in the spectrum relates to theelectron transition taking place in the atom.

The visible part of the hydrogen spectrum consists of a series of lines whichget closer together at shorter wavelengths (higher frequencies). It is knownas the Balmer series, after its discoverer. Fig. 37 is a diagram of the mainlines in this series.

There are more lines in this region,becoming closer together as .\ decreases -

M 0 N 0 O"lM r--<0 <O.,f c:i r...: co io <;f.\/nm __ -.ill ~._------~._--~~--MTO"l_.~-~rr_+--~~

red green violet ultra-violet

Fig.37 The Balmer series

Use the information from Fig. 37 to do the next exercise.

64

Exercise 65 Using the relationship A = c/v and Planck's equation~calculate the energy of the red line in Fig. 37.

h 6.63 x 10-34 J s

c = 3.00 X 108 m S-l


Planck's constant is sometimes quoted with reference to one mole of electrontransitions, i.e. 3.99 x 10-13 kJ s mol -1.

The energy you have just calculated is the energy needed to boost an electronfrom the second energy level to the third. It is given out as a quantum oflight, called a photon, when the electron drops back to the second level.Fig. 38 shows this electron transition (n=3 to n=2) with its correspondingspectral line; in addition, it shows transitions from higher energy levelsto the level n=2 and their corresponding spectral lines. At increasing7requencies, the lines get closer and closer until they merge.

t ----------------- -n=co~ n=7~ n=6~ n=5cQ)

-.-------------+----~--+_++_n=3

---------------,.------+---+-+-t- n = 4

n=2I II II II II II II II II II I

n=lI II II I

I I I I

I I IIn= 4 5 6 7co

A decrease ---.(" increase)

Fig. 38. Electron transitions and the Balmer series

Exercise 66 (a) What electron transition corresponds to thepoint where the spectral lines merge?

(b) What happens to the electron if n = oo?(c) Could you use the energy value at this point to calculate

a value for the ionization energy? Explain.(Answers on page 95 )

In the next section, we go on to look at the other series in the hydrogenemission spectrum.

65S2-0

The complete hydrogen emission spectrum

In this section, we show that each series in the hydrogen spectrum correspondsto a set of electron transitions starting and ending at a different energylevel. One of these series can be used to calculate ionization energy values.


(47) describe the emission spectrum of atomic hydrogen;(48) sketch at least one series of lines from the hydrogen spectrum;(49) explain how a hydrogen spectrum is produced.

If it is available, you should now watch the ILPAC videotape'The hydrogen spectrum' .

Read about the emission spectrum of hydrogen in a text-book.

The essential piece of apparatus, a discharge tube, containshydrogen at very low pressure. Look- for a description of howa discharge tube is used and the changes that take place insideit.

If the apparatus is available, your teacher may set up a demon-stration of the hydrogen emission spectrum for you. If so, youshould view it through a hand spectroscope and try and identifysome of the lines by comparing them with a photograph or Fig. 37.

The relationship between the various series of lines which go to make up thehydrogen spectrum is shown in Fig. 39. Each series is named after itsdiscoverer. You do not need to learn all these names, but you will find ituseful to remember Balmer and Lyman.

Pfund Paschen Balmerr"---. ~ ,------A----, Lyman

111111111111 I I 11111 I 1111~

Brackett

'A/nmco 700 400 200

ultra-violet

100

infra-red visible

Fig.39. The hydrogen spectrum

Study the diagram for a few moments and then use it to do the exercise whichfollows.

Exercise 67 (a) In what way are the other series in the hydrogenspectrum similar to the Balmer series?

(b) Give a simple explanation for this similarity,in terms of energy levels.


66

The pattern in the spectral lines has been described mathematically by theRydberg equation:

1X n: 2)

where A is the wavelength of the radiation in nmj RH is a constant~ theRydberg constant. Its value for the hydrogen spectrum is 1.0967758 X 107 m-l.nl and n2 are integers~ with the value of nl always being greater than n2.

n2 represents the electron shell to which the electron is dropping back andnl represents the electron shell to which the electron has been promoted.For a given series then~ n2 has a fixed value (in the Balmer series, n2 = 2)and nl has a range of values~ from (n2 + 1) to infinity.

Fig. 40 below shows the relationship between the main series in the hydrogenspectrum and the energy levels with which they are associated.

n=x~~~~~~:En=5==n=4 ----r-t-t----,--+-+-+---r--fl--+--+--...L...L".....J''-- Brackett series

n=3 -....-i-t-t----.--t-+-+-+--..1......I.~~-.1....-'--Paschen series

n=2 --.-+-+-I-I--4-+-t--+-+- Ba Imer se riesI I I I I, I I I I violet\ \ \ \ \I \ \ \ \ 490\ \ \\ \ II J\ \ \ ,", ..\ \ \ ", <; ?;\ \'" --- / / /" '-,'" .•...-----/ ",/ /" ,,------- //

", <, •••••---------/<,

<,<,

.•................. --- -------

500I

600I

red700

I

I/

//

//./",",---/'"---

wavelength/nm

n=1 --'--'--'-...•.....•- Lyman senes

Fig. 40. Electron transitions and the hydrogen spectrum

Use the diagram to help you answer the next exercise.

Exercise 68 Which series of lines in the hydrogen emission spectrum ~would be suitable for determining its ionization energyGive a reason for your answer. ~~(Answer on page 95 )

67

You may have been surprised that so far, in our study of the hydrogen emissionspectrum, we have related the spectral lines to electron transition betweenmajor energy shells in the atom, without mentioning sub-shells. There is agood reason for this. In the hydrogen atom, there is no difference in energybetween the sub-levels within a shell. However, in atoms other than hydrogen,the sub-shells are at different energy levels and we can easily demonstratetheir existence by emission spectra.

In such multi-electron atoms, many electron transitions, from one orbital toanother in different shells, or even within the same shell, are possible.These resul t in more complex emission spectra consisting of a great manylines.

It is possible to analyse a complex emission spectrum into a large number ofconverging series like those you have seen for hydrogen, but they are not soobvious because they overlap. At A-level, you will not be asked to interpretin detail anything more complex than the hydrogen spectrum.

In the final section of this Unit, we go on to see how the ionization energyof hydrogen can be calculated from frequency measurements of the appropriateseries of lines in its emission spectrum. The ionization energy of anyelement can be calculated using a similar method, but since the details aremore complicated, you need only know that it can be done in principle.

Convergence limits and ionization energyYou have noticed that the lines in each series in the hydrogen emission spec-trum get closer and closer together at higher frequencies. We now make useof this fact to calculate the ionization energy for hydrogen.

Objectives. When you hove finished this section you should be able to:

(50) explain what is meant by the convergence limit of a series of lines inthe hydrogen emission spectrum;

(51) calculate a value for the ionization energy of hydrogen by obtainingthe convergence limit graphically.

Read about convergence limits in the hydrogen spectrum and then do thefollowing exercise.

oW

Exercise 69 (a) Explain how the convergence limit of the Lymanseries can be used to provide a value for theionization energy of hydrogen.

(b) Why would the convergence limit of the Balmer orthe Brackett series not be suitable for determining theionization energy?


68

In the next exercise, we suggest graphical methods in which you can use thefrequencies of radiation emitted in the Lyman series to calculate a value forthe ionization energy of hydrogen.

Exercise 70 Table 10 shows the frequency of lines in the Lymanseries in the emission spectrum of hydrogen.Complete the table and then use the information toobtain the first ionization energy of hydrogen by oneof the methods below. We suggest you use method (ii)if your syllabus requires knowledge of the Rydberg equation.Table 10

Energy level, Frequency, V ~v 1n, of excited /1015 S-l /1015 S-l n2

electron

2 2.466} 0.4573 2.923} 0.1604 3.0835 3.1576 3.1977 3.2218 3.2379 3.248

The symbol b (Greek letter ldelta1) is used to refer to thedifference between two values of a physical quantity. ·Thus,bV = V2 - V1.

(a) EITHER(i) Plot a graph of ~V (vertical axis) against V (horizontalaxis). (You can use either the higher or the lower value ofV in each pair as long as you are consistent. Better still,plot two lines using both values in each pair.) Extrapolatethe curve to ~V = 0 and estimate a value of V at this point.OR(ii) Plot a graph of V (vertical axis) against 1/n2 (hori-zontal axis). Extrapolate the line to 1/n2 = 0 (i.e. n = 00)and estimate a value of V at this point.

(b) Use Planck's constant to calculate a value for the ioniza-tion energy from this frequency. Hint: ionization energyrefers to one mole of electrons.

(c) Compare the value you have calculated with the value givenin your data book for the first ionization energy of hydro-gen.

(d) If you used method (ii)1 explain how your plot relates tothe Rydberg equation. Obtain a value for the Rydbergconstant from the slope of the line and/or the intercept.


69

To help you draw together your ideas about the hydrogen spectrum andits use in determining the structure of the atoml do the Teacher-marked Exercise which follows. After you have looked through your I

notesl we suggest that you put them away and write your answer inexamination conditionsl allowing about half-an-hour.


The atomic spectrum of hydrogen is given by thefollowing relationship:

n~ 2 )

(a) (i) What does A represent?(ii) What do the terms nl and n2 represent?(iii) What are the units of the constant RH?

(b) The spectrum comprises a number of lines which may bedivided into a number of series.(i) Why does the spectrum consist of lines?(ii) Why is there a small number of series in thespectrum?(iii) Explain why each series converges and in whatdirection it converges.

(c) What method is used to generate the light source forobserving the atomic spectrum of hydrogen?

(d) Name the instrument used to resolve the hydrogen spectrum.

LEVEL TWO CHECKLISTYou have now reached the end of this Unit. Look again at the checklist atthe end of Level One. In additionl you should be able to:

(21) define first ionization energy;(22) & (23) describe how ionization energy is measured and calculated by an

electron bombardment method;(24) write equations representing secondl third and subsequent ionization

energies of a given element;(25) deduce the electron arrangement of an element from a graph of loglo

ionization energy against number of electron removed;(26) use a graph of successive ionization energy against number of electrqn

removed to provide evidence for the existence of subshells;(27) describe briefly what is meant by the wave-particle duality of an

electron;(28) give a simplel non-mathematical description of an orbital in terms of

probabili ties.;

70

(29) draw the shapes of an a-orbital and p-orbital;(30) state the maximum number of electrons that an orbital can hold;(31) to (33) use the aufbau principle to work out the order in which

orbitals are filled in a given element;(34) to (35) write down the electronic configuration of any element or ion

in the first fo~r periods of the Periodic Table using(a) the electrons-in-boxes method,(b) a, p, d, f notation;

(36) identify an element given values of successive ionization energies;(37) & (38) plot a graph of first ionization energy against atomic number

and use it to explain the term 'periodic';(39) explain the changes in first ionization energy that take place across

the second period;(40) describe the difference between a continuous spectrum and a line

emission spectrum;(41) explain the emission of light by atoms in terms of excited states;(42) to (46) state the relationship between

(i) wavelength and frequency,(ii) energy and frequency (Planck's relationship)and use them in calculations;

(47) & (49) describe the emission spectrum of atomic hydrogen and explainhow it is produced;

(48) & (50) sketch at least one series of lines from the hydrogen spectrumand explain what is meant by its convergence limit;

(51) calculate a value for the 'ionization energy of hydrogen by obtainingthe convergence limit graphically.

Check that you have adequate notes before going on to the End-of-Unit Test.

END-OF-UNIT TESTTo find out how well you have learned the material in this Unit,try the test which follows. Read the notes below beforestarting.1. You should spend about 1~ hours on this test.2. You will need a sheet of graph paper.3. Hand your answers to your teacher for marking.

71

END-OF-UNIT TEST \\\;lQuestions 1-3 concern the first six ionization energies for theelements A to E below:

1st 2nd 3rd 4th 5th 6th ionization energy (kJ mol-1)

A 1090 2350 4610 6220 37 800 47 000B 1400 2860 4590 7480 9400 53 200C 494 4560 6940 9540 13 400 16 6000 736 1450 7740 10 500 13 600 18 000E 1310 3390 5320 7450 11 000 13 300

Select from A to E, the element which is most likely to

1 . be in Group IV of the Periodic Table 0(1)2. form a chloride of the type MC12 (1)3. form a compound of the type Na2M (1)

In questions 4 to 6 inclusive, one, more than one or none of the suggestedresponses may be correct. Answer as follows:A if only 1, 2 and 3 are correctB if only 1 and 3 are correctC if only 2 and 4 are correct0 if only 4 is correctE if some other response, or combination, is correct.

4. From which of the following, TAKEN TOGETHER, can the ionizationenergy of hydrogen (in kJ mol-1) be calculated?1. The value of Planck's constant (in kJ mol-1 s).2. The value of the Avogadro constant.3. The frequency of the limit of convergence of the lines in the ultra-

violet emission spectrum of hydrogen (in S-l).4. The number of energy levels in the hydrogen atom. (1 )

73

5. The plot below shows the values of the logarithms of the firstfive ionization energies rlgCI.E.)] of an element X.

ui

xx

x

xx

Fig. 41.

This plot shows1. part of the evidence for the arrangement of the electrons of an atom

in energy levels or 'shells'2. that X cannot have an atomic number less than 123. that X could be an. element in Group 2 (an alkaline earth me~al)4. the rise in ionization energy with increasing average distance of the

electron from the nucleus (1)

6. Consider the following changes:

0I M (s) + M(g) IV M+(g) + M2+(g) + e-II MCs) + M2+Cg) + 2e- V MCg) + M2+Cg) + 2e-III M(g) + M+(g) + e-

The second ionization energy of M could be calculated from the energyvalues associated with1. I + V 3. III + IV2. V - III 4. II - I - III (1 )

Questions 7 and 8 are followed by five suggested answers. Select the bestanswer in each case.

7. The first ionization energy for carbon is greater than it is forsodium. One of the factors responsible is that theA nuclear charge on carbon is greaterB outer quantum shell is further from the nucleus in carbon atoms than

in sodium atomsC number of electrons in the outer quantum shell of carbon is greater

than in sodiumo shielding provided by the inner quantum shells in sodium is greaterE interatomic bonding in graphite and diamond is stronger than in

metallic sodium. (1)

74

8. The ground-state electronic configurations of five elements areshown below. For which element would you expect the value ofthe first ionization energy to be the greatest?

15 25 2p 15 25 2pA ITJOI I I 0 OJ] OJ] I I I I

OJ] 0 I8 E OJ] OJ] It I I Ic OJ][]I I I (1 )

For questions 9 and 10~ choose an answer from A to E as follows:A 80th statements true: second explains first8 80th statements true: second does not explain firstC First true: second falseo First false: second trueE 80th false

9.

First statementGaseous elements~ excited by ahigh-voltage electrical dis-charge~ emit light of charac-teristic colours.

10. The first ionization energiesof elements decrease down agroup of the Periodic Table.

Second statementWhen gaseous elements areexcited by a high voltageelectric discharge~ onlyenergies equal to thecharacteristic ionization energiesthe different elements are beingradiated.

In descending a group of thePeriodic Table~ the shieldingeffect of inner electron shellsincreases and the outermostelectron shell becomes furtherfrom the nucleus.

11. The first seven types of orbitals permitted for any atom are~in random order~ 2s~ 3p~4s~3d,1s~2p,3s.

If the atom is Ca, write down the orbitals in order of increasingenergy (from left to right) and give the number of electrons ineach orbital.

0of

(1 )

0(1)

0(2)

0(2)12. (a) Sketch a line spectrum of hydrogen (Lyman series only~wavelength increasing from left to right).

(b) The charge on the oxygen nucleus is eight times that ontne hydrogen nucleus and yet the first ionizationenergies of hydrogen and oxygen are almost identical (1300 kJ mol-1).

Suggest reasons for this (2)

75

13. In the table below~ the first~ second and third ionizationenergies of six successive elements in the Periodic Table arelisted. The elements have been arbitrarily denoted by theletters A to F. All energy values are given in kJ mol-1•

Table 11

A B C 0 E F

1st Ionization Energy 1013 1000 1255 1519 418 5902nd Ionization Energy 1904 2255 2297 2665 3067 11463rd Ionization Energy 2916 3389 3853 3933 4393 4916

(a) (i) Which one of the elements A to F is likely to be a noble gas?(ii) Give reason(s) for your answer. (2)

(b) In the light of your answer to (a)~ suggest the names of a set ofchemical elements that could be represented by A to F. (2)

(c) State the equation representing the processes to which the ioni-zation energies refer. Use the symbol Z to denote the element. (3)

(d) The first ionization energy of some elements may be determined by an'electron impact' method. The following is a schematic diagram ofthe apparatus used for this .

Fig. 42.

.#""'"0 -------~-..__r___.....s\. +

20v

3v_ + .._-----L...--....I...---......L...---/

(iJ Label the parts of the apparatus marked by letters P to S inthe diagram.(ii) What materials, if any, apart from the electrodes should becontained inside the tube? (1)(iii) Sketch a graph showing the approximate experimental resultswhich would be obtained with the apparatus. (Good labelling isimportant.) (3)

76

14.'11

I

, i-r- ;

I ,I

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The graph shows the first ionization energies of fifteen successiveelements in the Periodic Table, lettered A to 0, all with atomicnumbers less than 25.(a) Using the letters A to 0 as appropriate (and not the chemical symbols

which you know or think these letters represent) select:(i) two alkali metals (Group 1 metals);

(2 )(ii) an element which forms no true chemical compounds.(b) Although the graph shows an overall rise in first ionization energy

from element G to element N, the value for element I is lower thanfor element H. How may this be explained? (2)

(c) On graph paper, sketch the graphshowing the first six successiveionization energies of the elementG. (2)

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[2)

(e) Which of the elements A to 0 are inthe s-block and which in the p-block?

(2)

345ionization number

62Fig. 44.

77

15. (a) An isotope of uranium is represented by the symbol 2~~U.What is the significance of the two numbers?

(b) Identify A, B, C, 0 and E in the following equations:

(i) 2~~U ~ ex + A

(ii) 2~~U ~ S + B

(iii) 2~~U ~ Y + C

(iv) 238 + iH ~ 2~~U + 092

(v) 2~~U + 6n ~ ~~Mo + l;~La + 26n + 7E (6)

(c) In the reaction represented by equation (v), the product particleshave approximately 0.1% less mass than the reactant particles.What is the significance of this? (2)

16. Here is some information concerning element X, of atomic number31. In its natural state, it consists of a mixtur~ of two isotopesXA and.XB•

Table 12

Isotope Isotopic Percentagemass abundance

XA 69.0 60.2

XB 71 .0 39.8

Its first four ionization energies are 580, 2000, 3000 and 6200 kJ mol~ .(a) Calculate a value for the relative atomic mass of X correct to

three significant figures. (3)(b) (i) Write down the electronic configuration (in terms of s,p and

d levels) of element X in its ground state.(ii) In which group of the Periodic Table is X placed?

(c) Explain why:(i) The difference between the first and second ionization energiesis greater than that between the second and third ionization

(2)

energies. (2)(ii) The difference between the third and fourth ionization energiesis much larger than that between the other successive energies. (2)

(Total 60 marks)

78

APPENDIX ONE

A HISTORICAL PERSPECTIVESo far in this Unit we have nut included a historical account of the work whichled to the models of atomic structure we have outlined. This is partly becauseyou can understand something without knowing the details of its historicaldevelopment and partly because few examination boards require such knowledge.

However~ we hope you will be interested to read about some of the work that wasdone - particularly since the turn of the century - and consider its implica-tions for society today. In this appendix~ we give some outline notes andsuggestions for further reading. However~ our list is not exhaustive and newbooks are appearing all the time so you should see what is available in yourschool or local library.

Check with your teacher whether your examination board does require anyhistorical knowledge. As a guide~ we include some typical examination ques-tions in this subject area which you should try~ if appropriate.

Chronological table of some important developments in atomic theory

1803 - Oalton's theory of identical atoms1884 - Balmer observed the visible spectrum of hydrogen1896 - Becquerel discovered radioactivity1897 - Thomson discovered the electron1911 - Rutherford proposed the nuclear atom1913 - Moseley defined atomic number; Rutherford and Soddy discovered

isotopes; Bo~r's theory of planetary electrons in atoms1919 - Rutherford transmuted 14N to 170 by a-bombardment1932 - Chadwick characterised neutrons in beam from Be by a-bombardment1939 - Hahn and Strassmann discovered atomic fission1945 - Hiroshima and Nagasaki destroyed by fission bombs1952 - Nuclear fusion bomb (hydrogen bomb) at Bikini Atoll1956 - First nuclear fission power-station~ Calder Hall~ Cumbria1960's - Attempts to harness nuclear fusion (Sakharov and others)1970's - The hunting of the (alleged) quark

Some of the many books which you may find usefut are listed below:

Atomic structure

Asimov~ Isaac: Understanding physics; the electron~ proton and neutron.(Sdgne t , 1966)

79

[Jowing" Margaret: Reflections on atomic energy history. (Rede Lecture" 1978).0521 22392 X

Jones" Rotblat & Whitrow: Atoms and the universe. (Pelican" 1973).0140 215514

Oliver" H.P.H.:(Lon gma n" 1971 )

Inside the atom - Nuffield Chemistry background book.0140 82330 1

Stableford" Brian: The mysteries of modern science - Chapter 2(Routledge & Kegan Paul" 1977) 07100 86970

Nuclear energy

Bacon" Hilary & Valentine" John: Power corrupts. (Plufb Press" 1981).o 8610 43456

Croall, Stephen & Sempler, Kaianders: Nuclear power for beginners.(Beginners Books Ltd., Writers and readers Co-op., 1981) 0 906386 063

Patterson" Walter: Nuclear power. (Penguin" 1976). 0 1402 1930 7

Dalton's atomic theoryDalton was not the first to propose that matter was particulate rather thancontinuous. The Greek philosopher, Democritus, in 400 BC, suggested that therewere unsplittable particles which we now call atoms (from the Greek a = not,tomos = I cut) and in the 17th century Isaac Newton said "It seems probableto me that God in the beginning formed matter in solid, massy, hard, impene-trable, moveable particles, of such sizes, and figures" and with such otherproperties" and in such proportion, as most conduced to the end for which Heformed them".

However, Dalton was the first to base an atomic theory on experiment. At thebirth of modern chemistry in the late 18th century, when many new elementswere being discovered by Priestley, Scheele, Davy and others, John Dalton(working in Manchester) identified the "Laws of Chemical Combination by Weight",These included the law of conservation of matter .•.the law of constantcomposition and the law of multiple proportions; and they could be explainedby his atomic theory.

For further information on these laws, you should consult oldertextbooks. You may also be interested in trying experiments toillustrate the laws" in which case you should consult your teacher.

Dalton's theory had its weaknesses. He thought water was HO, he did not knowabout isotopes and he did not foresee the "splitting of the atom" by 20thcentury nuclear physicists.

Look at the propositions of Dalton's atomic theory and suggest how each onemight be modified in the light of modern knowledge. Bear in mind, however,that his simple 'model' of matter is still quite useful both as a firstintroduction to the subject and also in topics where a more sophisticatedmodel is not necessary. An example of the latter is the kinetic theory ofgases which you will study in a later Unit.

80

The discovery of the electronRead about the work of Crookes and J.J. Thomson on 'cathode rays'which they observed when an electrical discharge was passed througha gas at low pressure. The properties of these rays showed themto consist of particles, each very much smaller than an atom andwith a negative charge.

The Geiger-Marsden experimentGeiger and Marsden, working under the direction of Lord Rutherford, employeda stream of a-particles from a radioactive source for bombarding a thin sheetof gold or other metal. They found that most of the particles went straightthrough, but that a small fraction rebounded, as shown in Fig. 45.

beam of a particles deflected

fluorescent screen

deflected a particle

Fig. 45. The Geiger-Marsden experiment

Read about this experiment to understand how it showed that thematerial in gold atoms is concentrated in compact nuclei, likestones in plums. Rutherford suggested the nuclei were positivelycharged and the outer regions contained electrons of compensatingnegative charge and, as you have already learned, this model was furtherelaborated by Bohr and others.

Moseley's experimentIn 1913, Moseley showed that there were no gaps in the first forty or soelements in the Periodic Table. He obtained X-rays from each element in turnand found their frequencies by diffracting them, using a crystal of potassiumhexacyanoferrate(III) (also known as potassium ferricyanide), as shown inFig. 46.

stream ofelectrons

photographic plate

crystal

diffractionring, radiuscorrespondingto II

x- rays

Fig. 46. Moseley's experiment 81

Find out how the variation of the frequency of the X-rays with theidentity of the element showed that atomic number Z is a fundamentalcharacteristic of an element and not just the position of thatelement in a list. Also, look for the reasoning which showed thatthere were no gaps in the first forty or so elements in the Periodic

oCD

Table.

Together with the discovery of isotopes at about the same time, Moseley's workled to the search for the neutron which, however, was not finally identifiedfor nearly twenty years.

Consolidation

To consolidate your reading, you should now attempt the following [2Jteacher-marked exercise, which consists of parts of three A-level ~questions. This exercise is designed to help you organise yourideas about certain aspects of the history of atomic structure.Before you start writing, read through any notes you have made andcheck over any points you are not sure about in a suitable book.Then put away your notes and allow about 45 minutes to write an answer.


(a) Summarise the observations which led to thediscovery of the electron. On what experi-mental evidence is the electron regarded asbeing both particle-like and wave-like innature?

(b) For each of the following classical experiments,describe briefly what was done, what wasobserved, and what was deduced.(i) Geiger and Marsden's experiment;(ii) Moseley's experiment.

(c) Describe in outline how a beam of neutrons canbe produced. State briefly what experimentalevidence led to the conclusion that a neutronhas(i) no electric charge;(ii) a mass approximately equal to that of theproton.

82

APPENDIX TWO

The relationship between charge and energyIn Experiment 1, you used a conversion factor to obtain a value for the energyacquired by electrons when accelerated by a measured voltage. We now derivethis conversion factor.

It follows from basic definitions that one coulomb (1 C) of ~harge acceleratedby a potential difference of one volt (1 V) gains one joule (1 J) of energy,i.e. 1 C accelerated by 1 V gains 1 J.

The charge on an electron is 1.6 X 10-19 C:. 1 electron accelerated by 1 volt gains 1.6 x 10-19 J

There are 6.02 x 1023 electrons in 1 mol of electrons:. 1 mol of electrons accelerated by 1 V gains 1.6 x 10-19 x 6.02 X 1023 J

= 96300 J

The energy acquired by a single electron accelerated by one volt is sometimesreferred to as one electron-volt (ev), and ionization energies are sometimesquoted in electron-volts. The calculation above shows that:

!1 eV = 96.3 kJ mOl-1!

83

APPENDIX THREE

ADDITIONAL EXERCISESYou can use the exercises in this Appendix to give you extra practice in someof the types of calculation you have already met in the Unit. They may also beuseful for revision.

Calculating relative atomic mass from percentage abundanceExercise 71

Exercise 72

Exercise 73

Exercise 74

Chlorine consists of isotopes of relative masses 34.97and 36.96 with natural abundances of 75~77% and 24.23%respectively.Calculate the mean relative atomic mass of naturally-occurring chlorine.

Calculate the relative atomic mass of natural lithiumwhich consists of 7.4% of 6Li (relative atomic mass6.02) and 92.6% of 7Li (relative atomic mass 7.02).

Copper (atomic number 29) has two isotopes, the firstof relative atomic mass 62.9 and abundance 65%, thesecond of relative atomic mass 64.9 and abundance 35%.Calculate the mean relative atomic mass of naturally-occurring copper.

Using mass spectrometry, the element gallium has beenfound to consist of 60.4 per cent of an isotope ofatomic mass 68.93 and 39.6 per ce'rrt of an isotope ofatomic mass 70.92.Calculate, to three significant figures, the relativeatomic mass of gallium.

Answers to all the exercises in this section are on page 96.

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CONTRIBUTORS

Project Director

Colin Robertson , Inspector for Science , ILEA

Writing team

The materials were written and revised by practising teachers seconded to theProject for limited periods :

Lambros AtteshlisLesley BulmanMike FoleyAnn FriendLawrence HalsteadTerence Kelly

Production Team

Tony LanghamVanda ChanJohn SangwinPeter FaldonDawn DevereuxConstance Godfrey :Stella Jefferies

Frank McManusLeona rd RoselaarFran RoweAlec ThompsonSteve Wa xman

i/c production and cover designGraphicsAVA TechnicianAVA TechnicianOffice and typingTypingTyping and layout

Videotapes

Brian Babb, Producer, Educational Television Centre , ILEA

Reader

John Stephens , Department of Natural Sciences, South London College

Evaluator

John Gilbert , Institute for Educational Technology , University of Surrey

ILPAC trial schools

The following schools and colleges took part in the trials of the IndependentLearning Project for Advanced Chemistry . The Inner London Education Authoritywishes to thank the teachers in these schools and their students for their help .

Abbey Wood SchoolAcland Burghley SchoolBacon's C.E . SchoolBrooke House SchoolDunraven SchoolElliott SchoolEltham Hill SchoolEnsham SchoolForest Hill SchoolHighbury Grove SchoolHull College of Further EducationHydeburn School.

John Roan SchoolLadbroke SchoolLondon Nautical SchoolMorpeth SchoolNorth Westminster Community SchoolQuintin Kynaston SchoolSt . Mark's C.E . SchoolSydenham SchoolThomas Calton SchoolWalsingham SchoolWoodberry Down SchoolWoolverstone Hall

science;ilpac unit s2: atomic structure

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