chm3010_basic quantum theory 1 sem 1 09-10

8/4/2019 CHM3010_Basic Quantum Theory 1 Sem 1 09-10

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CHM 3010_Quantum 1 1

CHM 3010

Physical and InorganicChemistry


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Lecturers

DR. KAMALIAH SIRAT (COORDINATOR) DR. HASLINA AHMAD


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Pengenalan Diri

DR KAMALIAH SIRAT E-mail: [email protected] Pejabat: BSF 415 No. Tel: 03-89466787

Jika tiada: Tinggalkan pesanan utk temujanjipada masa lapang saya ikut jadual.
mailto:[email protected]:[email protected]


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Untuk Setiap Tajuk: 1

Subtajuk BBelajar

UUlang

FFaham

IIngat

LLatih

MMahir

a / / / / / /

b / / / /

c / / /

Sedikit Ilmu Untuk Dikongsi(Sumber: Dr Salihan Siais)


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ASSESSMENT TECHNIQUE

No. Assessment Technique %

1. Final Exam 40

2. Class Exams / Tests 30

3. Oral Presentation/project4. Class Participation /SCL 10

5. Lab report / Quizzes 20

100


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TESTS/Exams

TEST 1 14th October 2011 Wednesday 8.30-10.00 pm Basic Quantum Chemistry, Periodic Table, Main Group

Elements

TEST 2 18 th November 2011 Wednesday 8.30 pm Chemical bonding, Chemical Equilibrium,

Thermodynamic

Final Exam the rest of the topics (and all)


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SCL/Class presentation

10 % of total marks Groups Topics

Nuclear Chemistry Gas, liquid and solid


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Soft Skill (Kemahiran Insaniah)

You will be evaluated for KIbased on somecriteria


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Get Your Lab Schedule (kump 2)

Thursday (8-12), Teaching Lab

MP 8 (Makmal 440) and MP 9 (Makmal 442) Write down your names when getting the lab schedule

You will be divided into groups for your practical class Each of you will also be given a partner Make sure you know which lab you will be in

It is compulsory for all of you to have a lab coat and

a safety glass each


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Lab Regulations:

Be on time (5 minutes earlyno excuse) Wear your lab coat throughout Wear covered shoes Use safety goggles (except those already using

glasses)

Bring your own towel/tissue papers and matches Keep the lab clean and tidy always Arrange the stools neatly before leaving the lab Abide by all the general lab rules and regulations

Listen to and obey your demonstrators


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Report Writing: Page 1:

Name, Matric No., Lab No., Demonstrators Name, Day of Practical, Date ofPractical, Lecture Group, Lecturers Name

Page 2 Course Code and Name, Title of Experiment

Theory Materials Used Procedure in points form Results / data and Discussion Conclusion Suggestions

Answers to questions References


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Experiments and Reports

For most experiments, you will be doing them inpairs.

Only one ? report is required for each experimentbut the write up should be done alternately between

the partners You have to come to each practical class, prepared

with the outline of the report to be writtenand it willbe checked by the demonstrators

You are to finish the report on the same day You have to be in the lab for three hours.


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Try Your Best in Everything You Do

Practicals in the lab Be serious Read up before coming to the lab Prepare the lab report in the proper format in your lab

report book ? including the empty table if required for youto enter your data

Once you have obtained the data, you write the discussionand the conclusion.

In case your data are not as expected, you should be able

to explain why. No copying from previous reports.


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Skema Pemarkahan Laporan:

1. Muka surat pertama yang lengkap: 2 2. Tajuk percubaan: 2 3. Tujuan / Objektif: 4 4. Alat/Radas: 5 5. Pengenalan / Teori: 5 6. Bahan Kimia: 7 7. Kaedah: 8 8. Keputusan / data (disemak betul): 12 (+ 5) 9. Pengiraan: 15 10.Perbincangan: 13 11.Langkah berjaga-jaga: 2 12.Kesimpulan: 5 13.Rujukan: 5

14.Soalan: 10 Jumlah: 100

Siapkan rangka laporan sebelum ke kelas amali


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ReferencesReference:1. Whitten, Davis, Peck and Stanley, General

Chemistry, 7th Edition, 2004 (or Sameauthors, Chemistry, 8th Edition, 2007).

2. Brady and Senese, Chemistry: Matter andits changes, 4th Edition, 2004.

3. Silberberg, Chemistry, 3rd Edition, 2003.


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Introduction


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Philosophy

Art Science

Mathematics Physics Chemistry Biology

Analytical Physical Inorganic Organic

Physical and Inorganic Chemistry : CHM 30


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From Atom to .. Element - symbol Ions - symbol, charge Molecule - formula (correct ratio) Mixture - composition, separation Compound - composition, analysis Gas Liquid

Solid Reactionstoichiometry, balanced equation


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General Features of the Atom


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Properties of the Three Key Subatomic Particles

Charge MassRelative

1+

0

1-

Absolute(C)*

+1.60218x10-19

0

-1.60218x10-19

Relative(amu)

1.00727

1.00866

0.00054858

Absolute(g)

1.67262x10-24

1.67493x10-24

9.10939x10-28

Locationin the Atom

Nucleus

Outside

Nucleus

Nucleus

Name(Symbol)

Electron (e-)

Neutron (n0)

Proton (p+)


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Electron

Outside the nucleus Negatively charged

Particle Wave

Involved in most reactions Electron transfer Electron sharing


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Basic Quantum Theory 1


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Learning Outcomes: By the end of each of these topics

the students should be able to: Basic experiments of quantum theory

1. Relate atomic emission and absorption spectra to importantadvances in atomic theory.

2. Describe wave nature of electron 3. Describe the main features of the quantum mechanical picture of

the atom. Electronic structure

4. Describe the four quantum numbers, and give possiblecombinations of their values for specific atomic orbitals Orbital concepts, Geometry of electron clouds and Heisenbergs

uncertainty principle 5. Describe the shapes of orbitals and recall the usual order of their

relative energies

Aufbau principle, Paulis exclusion principle, Hunds rule andelectron configuration 6. Write the electron configurations of atoms 7. Relate the electron configuration of an atom to its position in the

periodic table


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Chapter Goals (Whitten: Chapter 5)

The Electronic Structures of Atoms10. Electromagnetic radiation11. The Photoelectric Effect

12. Atomic Spectra and the Bohr Atom13. The Wave Nature of the Electron14. The Quantum Mechanical Picture of the

Atom


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Chapter Goals(Whitten: Chapter 5)

15. Quantum Numbers16. Atomic Orbitals17. Electron Configurations18. Paramagnetism and Diamagnetism19. The Periodic Table and Electron

Configurations


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Throughout your study of the lecture, keep in mindthe following objectives, that you should be able to:

describe the properties of light

explain how the light emitted by an atom when it is excited

explain how the theoretical model of the electronic structure ofthe atom developed

Explain the relationship between the quantum numbers and theenergies of the electron waves in an atom

Give the symbols and allowed values for the three quantumnumbers n, l, ml, s

Recognise and draw the shapes of the different orbitals

Write the electronic configuration of elemental species (atoms,ions)


Perform the calculations involved.


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Modern Atomic TheoryATOM = nucleus (proton and neutron) and electron

For more than 3 centuries:to prove the presence of electron and nucleus

Theory of Classical Physics

Mechanics Optics Electricity Magnetic

Quantum Mechanics

Atom Molecular Structure Chemical Bonding



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The Quantum Mechanical Model of Atom

By the late 1800s it was clear that classical physics was incapableof describing atoms and molecules

Experiments showed that electrons acted like tiny chargedparticles in some experiments and waves in others

The physics that describes object with wave/particleduality is called quantum mechanics or quantumtheory

Energy can be transferred between things as light or radiation Radiation carries energy through space aswaves or oscillations moving

outward from a disturbance



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Electromagnetic radiation

Can you recall what is meant byElectromagnetic Radiation ?


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Electromagnetic radiation

A form of energy transferred through vacuum or medium (such

as air or glass) by means of wavelike oscillations of electric andmagnetic field. Electromagnetic waves (radiation) may be characterized by

their height or amplitude and the number that occur per second or frequency (v)

The units of frequency are the hertz (Hz)

The peak-to-peak distance is called the wavelength,

A

)second/(1s/1s1Hz1 -1


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Frequency and Wavelength

c = n


Distinction BetweenEnergy and Matter


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Electromagnetic Radiation

The wavelength of electromagnetic radiation has thesymbol .

Wavelength is the distance from the top (crest) of one waveto the top of the next wave. Measured in units of distance such as m,cm, . 1 = 1 x 10-10 m = 1 x 10-8 cm

The frequency of electromagnetic radiation has the symbol.

Frequency is the number of crests or troughs that pass agiven point per second.

Measured in units of 1/time - s-1

)second/(1s/1s1Hz1 -1


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CHM 3010_Quantum 1 36Physical and Inorganic Chemistry : CHM 30

is inversely proportional to n. Multiplication of and n is the radiation speed (speed of light).

n = c (2.998 X 108m s-1in vacuum)

Units: (m or nm); n [number of oscillation persecond (Hz or s-1)]


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Electromagnetic Spectrum

The wavelength of electromagnetic radiation range between 10-14 mto 102 m.

Violet

Indigo

Blue

Green

Yellow

Orange

Red

Gammaray

30cm

Frequency increases

Wavelength increases


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Example 1:

X-ray emitted by Cu is measured as having 1.54 10-10 m.

What is the frequency for this radiation?

What is the frequency for yellow radiation (wavelength

of 625 nm)?

The radio frequency of Light & Easy which is

broadcasted from Bukit Jalil, Kuala Lumpur through its

FM signal at 105.7 kHz.

What is the wavelength of the radio waves expressed in

meter?



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Example 2

Whitten 5-5: What is the frequency of green light of

wavelength 5200 ?

m105.2001

m10x1

)(5200

cc

7-10-

nn

1-14

7-

8

s105.77

m105.200

m/s103.00

n

n

c = n

1 = ? m


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Exercise 1-1

SOLUTION:PLAN:

Interconverting Wavelength and Frequency

PROBLEM: A dental hygienist uses x-rays (l= 1.00) to take a series of dentalradiographs while the patient listens to a radio station (l = 325cm)

and looks out the window at the blue sky (l= 473nm).What is the frequency (in s-1) of the electromagnetic radiation fromeach source? (Assume that the radiation travels at the speed oflight, 3.00x108m/s.)

wavelength in units given

wavelength in m

frequency (s-1 or Hz)

1 = 10-10m1cm = 10-2m1nm = 10-9m

n = c/

Use c = n

1.00A

325cm

473nm

10-10m1

10-2m1cm

10-9m1nm

= 1.00x10-10

m

= 325x10-2m

= 473x10-9m

n =3x108m/s

1.00x10-10m= 3x1018s-1

n

=

n =

3x108m/s

325x10-2m = 9.23x107

s-1

3x108m/s

473x10-9m= 6.34x1014s-1



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Experiments

Theories

Th diff i d b li h i h h dj li


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Figure 7.5

The diffraction pattern caused by light passing through two adjacent slits.

Indicates the wavelike nature of electromagnetic radiation


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Quanta of Energy

Black body radiation

Max Planck 1900, experiment: heating porous solid sphere, radiation emitted from dark part inside the solid. color of radiation changed from red to yellow finally white

depending on heating temperature.

He suggested that the energy of the emitted light isdiscontinuousand composed of tiny discrete packetscalled quanta. This was later called photon by Einstein.

Black body radiation (Planck) and photoelectric effect(Einstein) indicate that theelectromagnetic radiationis particle-like.


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Black body experiment by Planck: electromagnetic radiation could be viewed as a stream of tinyenergy packets or quanta we now call photons

To explain the energy spectrum it had to be assumedthat:

1. energy is quantized2. light has particle character

Plancks equation:

Energy

sJ10x6.626constantsPlanckh

hcor EhE

34-

n

E = hn

n= frequency for light


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Figure 7.6

Blackbody Radiation

DE = h n


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Photoelectric effect

Einstein observed ejection of electron when a metal

surface was subjected to light radiation. Electron wasejected only when the radiation energy exceed certainthreshold value. The energy of a photon is proportionalto its frequency. Photon was absorbed by the electron in

the metal only when the radiation frequency exceedcertain value.n threshold frequency


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The Photoelectric Effect

Light can strike the surface of some metalscausing an electron to be ejected.


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Albert Einstein (1905)

Einstein confirmed, that the energy of a photon isproportional to its frequencyand having the speed of light

both electrons and electromagnetic radiation can berepresented as either waves or particles

excited atoms can emit light

frequency intensity energy

E = mc2


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The Photoelectric Effect

What are some practical uses of the photoelectriceffect? Electronic door openers Light switches for street lights Exposure meters for cameras

Albert Einstein explained the photoelectric effect

Explanation involved light having particle-like behavior. Einstein won the 1921 Nobel Prize in Physics for this work.


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Energy of electromagnetic radiation

Energy of a photon = hn

Where h is proportionality constant known as Plancks constant (h =

6.63 X 10-34 J s)

Thus energyE = nhn where n = 1, 2, 3, ..integer.

Vibrated atom has energy of hn, 2hn, 3hn, , nhn. n is called quantumnumber.

When atom lost energy, a quantum of energy is released in form light.

2hn

3hn

hn

E ercise 1 2


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Whitten 5-6: What is the energy of a photon of

green light with wavelength 5200 ? What is theenergy of 1.00 mol of these photons?

photonperJ103.83E

)s10s)(5.77J10(6.626E

hE

s10x5.77thatknowwe5,-5ExampleFrom

19-

1-1434-

-114

n

n

kJ/mol231photon)perJ10.83photons)(310(6.022

:photonsofmol1.00For19-23

Exercise 1-2


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Electromagnetic Radiation and Motion

Molecules interact with electromagneticradiation. Molecules can absorb and emit light.

Once a molecule has absorbed light

(energy), the molecule can:1. Rotate2. Translate3. Vibrate4. Undergo Electronic transition

Describe theActions


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For water: Rotations occur in the microwave portion of spectrum. Vibrations occur in the infrared portion of spectrum.

Translation occursacross the spectrum. Electronic transitions occur in the ultraviolet portion of

spectrum.

Which movement requires the greatestenergy? Why do you say so?


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The atomic spectrum or emission spectrumis a series of individual lines called a linespectrum

Atomic SpectraElectric current excites & gives E to e-

Atoms emit energy, as e- return tolower E state

Emission and absorptionspectra of sodium atoms



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Flametests

strontium 38Sr copper 29Cu

Relate to Lamps NormallyFound in Everyday Life

NeonSodium

Fluorescence



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The atomic spectrum or emissionspectrum is a series of individual lines

called a line spectrum

Atomic spectra are unique for eachelement

Light emitted by

excited atoms is

comprised of a

few narrow beamswith frequencies

characteristic of

the element.

A i S d h B h A


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Atomic Spectra and the Bohr Atom

An absorption spectrumis formed byshining a beam of white light through a sampleof gas.

Absorption spectra indicate the wavelengths of light

that have been

absorbed.

A i S d h B h A


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Atomic and molecular spectra areimportant indicators of the underlyingstructure of the species.

In the early 20th century several eminent

scientists began to understand thisunderlying structure. Included in this list are:

Niels Bohr

Erwin Schrodinger Werner Heisenberg

A i S d h B h A


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Every element has a unique spectrum. Thus we can use spectra to identify

elements. This can be done in the lab, stars, fireworks, etc.

E l i h


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Early atomic theory

Rutherford, 1919:

nucleus of an atom contain particles with positive charge.However he did not indicate how electron is arranged aroundthe atom. According to classical physics if e- (-ve) ismotionless it will be easily attracted to the nucleus (+ve).

And if the e-

is continuously circulating the nucleus it willlose its energy and eventually spirally approach the nucleus. Thus, based on Rutherfords theory, the stability of atom is

unexplained.

-

+

Rydberg EquationEnergy & frequency, never more & never less


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Rydberg Equation

The Rydberg equation is an empirical equation that relates thewavelengths of the lines in the hydrogen spectrum(can be used to calculate all the spectral lines of hydrogen)

Atomic line spectra tell us that when an excited atom loses energy,not just any arbitrary amount can be lost

This is possible if the electron is restricted to certain energy levels The energy of the electron is said to be quantized

= RHRydberg equation -

1

1

n22

1

n12

n2 > n1, (n refers to the numbers of the energy levels in the emission spectrumof hydrogen RH is the Rydberg constant = 1.097 x 107m-1 or 109,678 cm-1



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Figure 7.9 Three series of spectral lines of atomic hydrogen

for the visible series, n1 = 2 and n2 = 3, 4, 5, ...

Bohrs Atomic Model


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J1018.2 182

2

2

42

222

42

h

me

n

b

hn

me

b

E

The first theoretical model that successfully accountedfor the Rydberg equation was proposed in 1913 by Niels

Bohr Bohr proposed that electrons move around the nucleus along

fixed paths or orbits much like the planets moving around the sun

The orbits, labeled with the integer n, have energy This equation allows the calculation of the energy of any orbit

Bohr s Atomic Model


Bohr Atomic Model


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Quantum staircaseContinuous (a) and discrete (b) potential energy of a tortoise.The potential energy of the tortoise in (b) is quantized.

Bohr Atomic Model


A i S d h B h A


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In 1913 Neils Bohr incorporated Plancksquantum theory into the hydrogen spectrumexplanation.

Here are the postulates of Bohrs theory.

1. Atom has a number of definite and discreteenergy levels (orbits) in which an electronmay exist without emitting or absorbing

electromagnetic radiation.As the orbital radius increases so does the energy1


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postulates of Bohrs theory.

2. An electron may move from one discreteenergy level (orbit) to another, but, in sodoing, monochromatic radiation is emittedor absorbed in accordance with thefollowing equation.

EE

hchEE-E

12

12

D

n

Energy is absorbed when electrons jump to higher orbits.

n = 2 to n = 4 for exampleEnergy is emitted when electrons fall to lower orbits.

n = 4 to n = 1 for example

l f B h h


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postulates of Bohrs theory.

3. An electron moves in a circular orbit aboutthe nucleus and it motion is governed bythe ordinary laws of mechanics andelectrostatics, with the restriction that the

angular momentum of the electron isquantized (can only have certain discretevalues).

angular momentum = mvr = nh/2h = Plancks constant n = 1,2,3,4,...(energy levels)v = velocity of electron m = mass of electronr = radius of orbit

Bohrs atomic model


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Bohr s atomic model

Bohr likened e around the nucleus as planet circling the sun. Electron

moves along fixed path called orbit.

+

n=1n=3 n=2

absorption

emission

Cross section of H atom. Nucleus atthe centre and electron occupies theorbit with lowest energy (n=1 for Hatom). Electron is excited to a higherlevel when energy is absorbed. The

higher levels are unstable and e dropto lower levels and energy is releasedin form of light emission.

Bohr predicted the radius of each orbit as:

rn = n2ao where ao = 0.53 (53 pm)(Bohr radius)

The series of spectral lines of atomic hydrogen


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p y g

for the visible series in hydrogen spectrum

Lyman n1 = 1 n2 = 2,3,4,,

Balmer n1 = 2 n2 = 3,4,5,,Paschen n1 = 3 n2 = 4,5,6,,Brackett n1 = 4 n2 = 5,6,7,,Pfund n1 = 5 n2 = 6,7,8,,


Figure 7.11


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The Bohr explanation of the three series of spectral lines.

Atomic Hydrogen Spectrum


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Atomic Hydrogen Spectrum

Example

Measure the wavelength of the third line in Brackett series for atomic

hydrogen spectrum?

n1 = 4, n2 = 4 + 3

Answer : = 2166.12 nm

Balmer, n1 = 2

1 = RH 1 - 1 RH = 109 678 cm-1

22 n22

n2 = 3, = 656.4 nm

n2 = 4, = 486.3 nm

n2 = 5, = 432.4 nm


Exercise 1-3


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Whitten 5-7: An orange line of wavelength5890 is observed in the emission spectrumof sodium. What is the energy of one photonof this orange light?

Lets do it !



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J10375.3m10890.5

m/s1000.3sJ10626.6

hchE

m10890.5

m1015890

197

834

7-10

n

m10890.5

m101

5890

7-10

n

hchE

m10890.5

m1015890 7

-10

m10890.5

m/s1000.3sJ10626.6

hchE

m10890.5

m1015890

7

834

7-10

n

Exercise 1-4


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Example 5-8. What is the wavelength of lightemitted when the hydrogen atoms energychanges from n = 4 to n = 2?

2d4


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16

1

4

1m101.097

14

1

2

1m101.097

1

n

1

n

1R

1

2nand4n

1-7

22

1-7

22

21

12


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m104.862

m102.0571

1875.0m101.0971

0625.0250.0m101.0971

7-

1-6

1-7

1-7



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Notice that the wavelength calculated from

the Rydberg equation matches the wavelengthof the green colored line in the H spectrum.



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p

Light of a characteristic wavelength (and

frequency) is emitted when electrons movefrom higher E (orbit, n = 4) to lower E (orbit,n = 1). This is the origin of emission spectra.

Light of a characteristic wavelength (andfrequency) is absorbed when electron jumps from

lower E (orbit, n = 2) to higher E (orbit, n= 4) This is the origin of absorption spectra.
http://d/Media/PowerPoint_Lectures/PowerPoint%20Media/Movies/07M07AN1.MOV


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Absorp

tion E

m

ission

Bohrs Atomic Theory
http://d/Media/PowerPoint_Lectures/PowerPoint%20Media/Movies/07M07AN1.MOV


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Successconfirmed the Rydberg equation

correctly explains the H emission spectrum (able to explain

the line spectrum of hydrogen atom and other ionic species

(such as He+, Li2+, Be3+,) with one electron.)Bohr has introduced the concept of quantum numbers and

fixed energy levels which are important step forward in atomic

theory.

made significant contribution to the development of theatomic theory (basis for the Modern Atomic Theory)

introduction to the mechanic quantum (integer)

y


Limitations


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Limitations

not able to account for atoms with more thanone electron and all attempt to modify it fail

(not an adequate theory)

Line spectrum


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p

White light from a tungsten filament is passed through prism, it givescontinuous spectrum of colors (rainbow). However when a gas is heated, a

line spectrum is obtained which composed of lines of certain colors(wavelength). For example when hydrogen gas is heated several lines invisible range i.e. red, blue, green and violet are observed.

Balmer showed that in this range

Where n is integer

122

7 1

2

110097.1

1

mn
http://d/Dr%20Asmah/Backup/Pengajaran/Pengajaran%20lalu/I%202004-05/CHM3010/Dr%20Zul/Brady%20Chem/183729.JPGhttp://d/Dr%20Asmah/Backup/Pengajaran/Pengajaran%20lalu/I%202004-05/CHM3010/Dr%20Zul/Brady%20Chem/183729.JPGhttp://d/Dr%20Asmah/Backup/Pengajaran/Pengajaran%20lalu/I%202004-05/CHM3010/Dr%20Zul/Brady%20Chem/183729.JPGhttp://d/Dr%20Asmah/Backup/Pengajaran/Pengajaran%20lalu/I%202004-05/CHM3010/Dr%20Zul/Brady%20Chem/183729.JPG


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The lowest energy state of an atom iscalled the ground state (an electron withn= 1 for a hydrogen atom)

Absorption and emission

of energy by the hydrogen

atom. An electron thatabsorbs energy is raised to

a higher energy level. A

particular frequency of

light is emitted when anelectron falls to a lower

energy level.


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An electron that escapes from thenucleus has infinity for its quantum numberand zero energy

Bohrs (theoretical) equation explains the(empirical) Rydberg equation

2222

22

1111

11

or

with

)(

hl

hl

lh

nnhc

b

lhnn

n

b

n

b

lh

hc

nnb

EEE

D


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The combination of constants, b/hc, has avalue which differs from the experimentally

derived value of RH by only 0.05% Bohrs efforts to develop a general theory

of electronic structure was doomed by the

wave/particle duality of electrons De Broglie suggested that the wavelength

of a particle of mass mmoving at speed v

ismv

h


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This relation provides the link between thedescription as a particle and as a wave

Heavy objects have very shortwavelengths so their matter waves and thewave properties go unnoticed

Tiny particles with small masses havelong wavelengths so their waveproperties are an important part of their

behavior Waves combine in two ways


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End of Particle Theory ofElectron

Wave Theory of Electron


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CLASSICAL THEORY

Matter

particulate,massive

Energy

continuous,wavelike

Since matter is discontinuous and particulate

perhaps energy is discontinuous and particulate.

Observation Theory

Planck: Energy is quantized; only certain valuesallowed

blackbody radiation

Einstein: Light has particulate behavior (photons)photoelectric effectBohr: Energy of atoms is quantized; photon

emitted when electron changes orbit.atomic line spectra

Figure 7.15

Summary of the major observationsand theories leading from classicaltheory to quantum theory.

Figure 7.15 continued


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Since energy is wavelike perhaps matter is wavelike

Observation Theory

deBroglie: All matter travels in waves; energy ofatom is quantized due to wave motion ofelectrons

Davisson/Germer:electron diffractionby metal crystal

Since matter has mass perhaps energy has mass

Observation Theory

Einstein/deBroglie: Mass and energy areequivalent; particles have wavelength andphotons have momentum.

Compton: photonwavelength increases

(momentumdecreases)

after colliding withelectron QUANTUM THEORY

Energy same as Matterparticulate, massive, wavelike

chm3010_basic quantum theory 1 sem 1 09-10

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