chapter 6 electronic structure of atoms

ElectronicStructureof Atoms

Chapter 6Electronic Structureof Atoms

Chemistry, The Central Science, 10th editionTheodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten

John D. BookstaverSt. Charles Community College

St. Peters, MO 2006, Prentice Hall, Inc.


6.1The Wave Nature of

Light


Light

• Much of our understanding of electronic structure of atoms comes from analysis of the light absorbed or emitted by substances

• The light that we see as colors is only a very small portion of the electromagnetic spectrum


Radiant Energy

• Electromagnetic radiation is also know as radiant energy because it carries (or radiates) energy through space

• Although each type of radiant energy is unique, they all share certain fundamental characteristics…They all behave as waves with

wavelike properties


Waves

• wavelength () = distance between corresponding points on adjacent waves crest to crest, trough to troughunits of meters (m) or nanometers (nm)

• amplitude = height of the wave


Waves• frequency ( ) = the # of

complete wavelengths, or cycles, passing a given point per unit of time units of s–1 or hertz (Hz)

• For waves traveling at the same velocity, the longer the , the smaller the and are inversely

proportional (as one increases, the other)

Short = High

Long = Low


• All radiation moves through a vacuum at the same velocity:

speed of light (c) = 3.0 x 108 m/s

• This common speed allows and to have a quantitative relationship c =

Shared Characteristics of Radiant Energy


The Electromagnetic Spectrum


• Which of the following has the highest frequency? Ultraviolet (UV) waves or Infrared (IR) waves?

• Which type of radiation has the longest wavelength? Visible light (VIS) or microwaves?

• Which color of light has the shortest wavelength, and thus highest frequency?

Concept Questions:

violet


6.2Quantized Energy and

Photons


• While the wave model explains many aspects of the nature of light, there are several phenomena it does not explain


The Nature of Energy

• It doesn’t explain how an object can glow when its temperature increases (blackbody radiation) or why the color of the glowing objects varies with the temperaturered-hot objects are

cooler than white-hot


The Nature of Energy• Max Planck physicist who

explained the relationship between temperature, light intensity, & wavelengths of emitted radiation

• Planck assumed energy could only be released or absorbed by atoms in discrete “chunks” called quanta (the smallest quantity of energy emitted/absorbed by radiation)


• A single quanta has a distinct amount of energy as given in the following equation: E = h h = 6.63 10−34 J•s (Planck’s constant)

• Since energy is emitted or absorbed in discrete chunks, energy can only be absorbed/released as a whole # multiple of Plank’s constant x frequencyh , 2h, 3h Since energy is restricted to multiples only, it is

said to be quantized (staircase analogy)

Quantized Energy & Quantum Theory


Photoelectric Effect

• In 1905, Einstein used Planck’s quantum theory to explain the photoelectric effect.In experiments, it was observed that light shining on

a clean metal surface causes e– to be emittedFor each unique metal, light below a minimum

threshold frequency resulted in NO e– being emitted


Photoelectric Effect• The details of this effect contradicted classical

physics which says radiation acts as wavesWave theory cannot predict why frequency is the

crucial factor for electron emission (wave theory supports that intensity of light would be the main factor but even the most intense light at a low frequency will not emit e–)

• Einstein explained the photoelectric effect by assuming that light is made up of photons (particles) each with an energy given by, E = h

http://phet.colorado.edu/en/simulation/photoelectric

http://phet.colorado.edu/en/simulation/photoelectric


The Nature of Energy

• Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:

c = E = h


Practice Question:• A photon of energy has a frequency of 4.13

x1014 Hz. What is the wavelength, in nanometers, of this photon. What color of the visible spectrum would it appear to be?

• c = = 3.0 x 108 m/s 4.13 x1014 Hz

= 7.26 x 10-7 m 109 nm = 726 nm = red 1 m


Practice Question:• The red light from a helium-neon laser has a

wavelength of 633 nm . What is the energy of one photon?

• c = and E = h l = 633 nm 1 m = 6.33 x 10-7 m

109 nm

E = hc = (6.63 x 10-34 Js)(3.0 x 108 m/s)

6.33 x 10-7 m

= 3.14 x10-19 J


6.3Line

Spectra + Bohr Model


Q1: The Nature of Energy

Another mystery that could not be explained by wave theory involved the emission spectra observed from energy emitted by atoms and molecules.


Q1: Continuous Spectra

• Some sources of radiation emit a single wavelength (laser)This radiation is monochromatic (of one color)

• Most radiant energy emits several wavelengths at once (lightbulbs = white light = all colors and wavelengths reflected)When this type of radiation is sent through a

prism, it is separated into its component wavelengths (forms a continuous spectrum of the rainbow)


Q1: Line Spectra• Not all radiation produces a continuous

spectrum of colorsWhen gases are placed under pressure in a tube

(and electricity is applied) the gases emit different colors of light (sodium = yellow, neon = red-orange)

When this light is passed through a prism, the result is a spectrum containing only a few specific wavelengths (this is known as a line emission spectra)

Every gas has a unique line spectra often referred to as it’s “fingerprint”


Line Spectra


• Niels Bohr assumed e– moved around the nucleus in distinct circular paths called orbits (aka: planetary model)Each orbit around the nucleus

has a different “n” value (known as the principle quantum number) • As “n” increases, so does

the radius size of the orbit and the distance of the orbit from the nucleus

Q2 & 3: Bohr Model of the Atom


Q2,3,&4: Bohr Model of the Atom• Each orbit has a specific quantity

of energy which increases as the value of “n” increases Bohr, like Planck, believed

energy was quantized• n = 1 is the lowest energy level; e–

in this orbit are known as ground state e– and are the most stable

• When electrons are in higher energy level (n = 2 through 7) they are called excited state e–


Q2 & 4: Electron “Jumping”• According to Bohr, electrons can “jump”

between energy levels only if the exact amount of energy needed was gained or lost by the e– (like rungs on a ladder)

• e– demotion = moving from higher lower “n” will emit radiant energy (energy released)

• e– promotion = moving from lower higher “n” will absorb radiant energy (energy required)


The Rydberg Equation

The energy absorbed or emitted (ΔE) from the process of electron “jumping” can be calculated by the equation:

E = −RH ( )1nf

2

1ni

2-

• RH = Rydberg constant = 2.18 10−18 J

• ni and nf = initial and final energy levels of the e– e– demotion = - ΔE e– promotion = + ΔE


Explanation - Line Emission Spectra• The specific spectral lines seen when an

element’s radiant energy is separated through a prism can mathematically be related to the Rydberg equation Thus, the existence of these spectral lines is

due to the quantized jumps made by e– between energy levels

Since each element has a different # of e– (in different energy levels), the energy of each “jump” will be different, resulting in unique (and colors) for every element = unique line emission spectra!!!


Q5: Limitations of Bohr Model• Bohr model offers an accurate explanation for the

Hydrogen line emission spectra (b/c it only has one e–), but does not as accurately apply to the spectra of other atoms

• Also, his model only views the electron as a particle and ignores the wavelike properties that exist

• Thus, the Bohr model was only a step towards a more comprehensive atomic model, but it did produce two significant ideas:

1) electrons can only exist in discrete energy levels

2) energy is involved in moving electrons between the energy levels


6.4The Wave

Behavior of Matter


• Louis de Broglie postulated that if light can behave as particles of matter, then matter should also be able to exhibit wave properties (“matter waves”)Ex) e– moving about the nucleus as a wave would

have characteristic wavelength & frequencyThe (in m) of any matter would depend on its

mass (in kg) & velocity (m/s)

For matter with an ordinary mass (even just a golf ball) the would be so tiny it would be imperceptible

Q1: The Wave Behavior of Matter

= hmv

1 J = 1 kg•m2

s2


The de Broglie Equation

Determine the wavelength of the following:

a) A 7000 g bowling ball rolls with a velocity of 8.0 m/s.

= 6.63 x 10-34 J•s = 1.18 x 10-35 m

(7.0 kg)(8.0 m/s)

b) What is the wavelength of an electron moving at 5.31 x 106 m/s? The mass of an electron is 9.11 x 10-31 kg

= 6.63 x 10-34 J•s = 1.37 x 10-10 m

(9.11 x 10-31 kg)(5.31 x 106 m/s)

=h

mv

http://www.youtube.com/watch?v=JIGI-eXK0tg




Proof of de Broglie Theory• A few years after his proposed theory,

experimental results backed de BroglieElectrons passed through a solid crystal and were

diffracted (broken up around slits just like a beam of light)

The double-slit experiment, demonstrates that matter and energy can display characteristics of both waves and particles

This technique leads to the development of the electron scanning microscope

http://www.youtube.com/watch?v=MTuyEn-ngIQ

http://www.youtube.com/watch?v=MTuyEn-ngIQ


Chicken Embryo; Termite; Dust Mite; Spider


Q2: The Uncertainty Principle• The dual nature of matter places a fundamental

limitation on how accurately both the speed and position of an object can be knownThis limitation becomes important only when matter is

of subatomic size

• Werner Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known:Therefore, it is impossible to know both the

location and momentum of an electron

(x) (mv) h4

The smaller the mass, the more uncertainty there is in its position

http://www.youtube.com/watch?v=32oUlB2BfEA

http://www.youtube.com/watch?v=32oUlB2BfEA


Bohr’s Model… incorrect• Why does the Bohr model of the atom violate

the uncertainty principle?• Bohr thought e– traveled in orbits

this cannot be true, b/c then the exact path and position of an e– would be known at all times

• De Broglie’s hypothesis and Heisenberg's uncertainty principle set the stage for a new model of the atomRecognizes the wave nature of e– and the

distinct energy levels that Bohr founded to describe the probable location of an e–


Quiz Review: 6.1 – 6.4• List all 7 types of radiation on the EM Spectrum in

order of increasing frequency.Radio, Microwaves, IR, Visible, UV, X-rays, Gamma rays

• There is a(n) ____________ relationship between wavelength and frequency.

• Energy and frequency are _____________ proportional to one another, meaning as one increases, the other _____________.

• The units for: Frequency: _______________ Wavlength: _______________ Energy: ______________

indirect

directly

increases

Hz = s-1

m or nm

J


Quiz Review: 6.1 – 6.4• Important Equations to MEMORIZE (constants will

be given) c = = E h [Rydberg]

E = hc = h

E = −RH ( )1nf

2

1ni

2-

• Continuous spectra vs. line spectra• Photoelectric effect – Einstein proved that waves behaved as particles• Bohr model of the atom

Energy levels/orbits, ground state vs. excited state Useful parts of the Bohr model?

• Absorbtion/Emissison of energy & electron jumping (relationship to quantized energy

• Heisenberg’s Uncertainty Principle – how does Bohr’s model violate this principle?


6.5Quantum Mechanics & Atomic Orbitals


Quantum Mechanics• In 1926, Erwin Schrödinger developed an equation

(Schrodinger’s wave equation), which incorporated both the wave and particle natures of matter

• This new way of dealing with subatomic particles is known as quantum mechanics.

http://www.google.com/url?sa=i&rct=j&q=schrodinger+wave+equation&source=images&cd=&cad=rja&docid=4KsKBdU5Gb8nKM&tbnid=JIexAB5nD6qFSM:&ved=0CAUQjRw&url=http://www.ck12.org/user:eWVvbWFubWlrZUBzYXlkZWwubmV0/section/Characteristics-of-Matter/&ei=_cIJUd_ZGIra0QHftIHICg&bvm=bv.41642243,d.dmQ&psig=AFQjCNFv79zoyo2gTGdiLnJVo2HYwTn3WA&ust=1359680602453098


Quantum Mechanical Model• Applies Heisenberg’s

uncertainty principle and distinct energy levels from Bohr model

• The quantum mechanical model of the atom statistically describes a general region of space around the nucleus where an electron is likely to be found at any given instant


Electron Density Distribution• From Schrodinger’s

wave equation, locations around the nucleus with the highest density of plotted “dots” represent the areas around the nucleus where an e– is most likely to be found


Quantum Numbers

• Mathematically solving the wave equation gives a set of wave functions (aka: orbitals) and their corresponding energies.

• Each orbital …describes the distribution of electron

density in space.has a characteristic energy & shape

• An orbital is described by a set of three quantum numbers.


Principal Quantum Number, n• Also seen in Bohr model, this quantum

number describes the energy level in which the orbital resides.

• n values are positive integers (starting at 1) • As n increases…

the orbital become larger e– spend more time further from the

nucleus e– have a higher energy


Azimuthal Quantum Number, l

• This quantum number defines the shape of the orbital

• Values of l are integers ranging from 0 to n − 1.

• We use alphabetical letters (s, p, d, f) to

communicate the different values of l and, therefore, the shapes and types of orbitals (seen in section 6.6)


Magnetic Quantum Number, ml

• Describes the three-dimensional orientation of the orbital (how the shape is oriented in space)

• Values are integers ranging from -l to l :

−l ≤ ml ≤ l• Therefore, on any given energy level,

there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.


Quantum NumbersValue of n 1 2 3 4

Value of l(n-1)

0 1 2 3

Type of orbital s p d f

Value of ml

(-l l )

0

(1)

-1, 0, 1

(3)

-2, -1, 0, 1, 2

(5)

-3, -2, -1, 0, 1, 2, 3

(7)


• Orbitals with the same principle quantum number, n, form an electron shell.

• Different orbital types within a shell are subshells 1s; 2s, 2p; 3s, 3p, 3d; 4s, 4p, 4d, 4f

Table 6.2


Practice:• What is the designation for the subshell

with…n = 5 and l = 3?n = 3 and l = 2?

• How many magnetic quantum #s (ml ) are involved in each subshell? Label them n = 5 and l = 3? n = 3 and l = 2?

… 5f

… 3d

… 7 = -3, -2, -1, 0 , 1, 2, 3

… 5 = -2, -1, 0 , 1, 2


6.6Representat

ions of Orbitals


Orbital Shapes• Recall…the shape of an orbital is described

by its azimuthal quantum #, l• l = 0 = s

every n value has an l of 0, thus an s orbital

• l = 1 = p only n = 2 or above has an l of 1, thus a p orbital

• l = 2 = d only n = 3 or above has an l of 2, thus a d orbital

• l = 3 = f only n = 4 or above has an l of 3, thus a f orbital


s Orbitals

• Lowest energy orbitals• Spherical in shape• Radius of sphere

increases with increasing value of n


s OrbitalsGraph - 6.18: Probability of finding an e– Vs. distance from the nucleus…

s orbitals possess nodes, which are regions where there is zero probability of finding an e–

The likelihood of finding e– further from then nucleus increases as the n value increases


p Orbitals• “dumbbell” shaped

e– density concentrated on either side of the nucleus (two lobes with a node between them)

• Since there are 3 ml values for p orbitals, there are 3 orientations in space (px, py, pz)For the same n value, each orientation is the same size

& of equal energy (larger n = bigger & more energy)


d Orbitals• There are five d

orbital orientations4 of them have 4

lobes like “four-leaf clovers”

the 5th resembles a p orbital with a doughnut around the center.

For a given n, all 5 orientations have equal energy (orbitals w/same energy are known as degenerate)


f Orbitals• There are seven f orbital orientations

For a given n, all 7 orientations are degenerate (have equal energy)

http://www.google.com/url?sa=i&rct=j&q=f+orbitals+shape&source=images&cd=&cad=rja&docid=Uru4r1eBHA2gmM&tbnid=RhUDTGDr0pz2LM:&ved=0CAUQjRw&url=http://www.angelfire.com/falcon2/dirgni/orbitals.html&ei=9zULUbPVD6Sn0AHQmoDACg&bvm=bv.41867550,d.dmQ&psig=AFQjCNE_eTA3YbGW-BxK51EtEG_xVjqMcg&ust=1359775603995654


6.7Many-

Electron Atoms


Energies of Orbitals• In a hydrogen atom, (where there is only one e–)

all the orbitals with the same n value have the same amount of energy regardless of orbital shape (s, p, d, & f are degenerate)

http://www.google.com/url?sa=i&rct=j&q=hydrogen+atom+energy+level+diagram&source=images&cd=&cad=rja&docid=u-hj4HNstPkenM&tbnid=pofPZT78JFByTM:&ved=0CAUQjRw&url=http://look4chemistry.blogspot.com/2011/03/electronic-configuration.html&ei=J0QLUb7EEsOZ0QGwm4CADQ&bvm=bv.41867550,d.dmQ&psig=AFQjCNFkslWNpSlAGNZQpDEhrySwosly1w&ust=1359779133547978


Energies of Orbitals• For multi-electron atoms, as the # of e–

increases, so does the repulsion between them.• Therefore, in multi-electron atoms, orbitals of the

same n energy level are NOT degenerate.

http://www.google.com/url?sa=i&rct=j&q=orbital+energy+diagrams&source=images&cd=&cad=rja&docid=EuDW5UArhLoBlM&tbnid=I71JSyH0kNja2M:&ved=0CAUQjRw&url=http://kaffee.50webs.com/Science/activities/Chem/Activity.Electron.Configuration.html&ei=vEULUbroJ-aL0QGikYGQDA&bvm=bv.41867550,d.dmQ&psig=AFQjCNH1dXKQTieSM3U0fveT1Ynehg0VSw&ust=1359779620339229


• The energy of the orbital increases as the l value increasesEnergy for a

given n value is, s < p < d < f

* notice, all five 3d orbitals are still degenerate (same energy level) but 3s < 3p < 3d

Energy Level

Diagram


• In the 1920s, it was discovered that 2 e– in the same orbital, say a 2s, do not have exactly the same energy.

• The “spin” of an e– describes the direction it spins in a magnetic field, which affects its energy.This lead to 4th quantum #

• The spin quantum number has only 2 values: +1/2 and −1/2

The 4th Quantum Number:Spin Magnetic Quantum Number, ms


Pauli Exclusion Principle• NO two e– in the same

atom can have the same set of all 4 quantum numbers n, l, ml , ms

Each orbital may hold a maximum of 2 e–, provided they have opposite spins (ms

values)Ex) A 3px orbital has the

same n, l, ml values but one e– must be +1/2 & one -1/2 to exist in the same orbital


Orbitals & Electrons in Sublevels

Sublevel # Orbitals Max # electrons

s 1 2

p 3 6

d 5 10

f 7 14

* Each orbital can hold a max. of 2 e–


6.8 - 6.9Electron Configurati

ons


Three rules are used to build the electron configuration:

Pauli Exclusion Principle

Aufbau principle

Hund’s Rule


• An orbital can hold only a max. of two electrons and they must have opposite spins.

• Electron Spin: +1/2 or -1/2

Pauli Exclusion Principle


Aufbau Principle

• Electrons occupy orbitals of lowest energy first.

Generally, as n increases, the energy increases and s < p < d < f

However, this is not always the case…


Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f


Diagram:Orbital Filling


Blocks in the Periodic Table


Hund’s Rule

• For degenerate orbitals (ex: the three p, five d, or seven f orbitals), the most stable atom (lowest energy) is attained when the number of e– with the same spin is maximized• e– fill orbitals with parallel spins before

paring up

Analogy: Students fill each seat of a school bus, one person at a time, before sitting together.


Types of Electron Configurations

• Orbital Diagrams shows electrons filling the sublevels in ordereach box represents one orbital subleveluses arrows to represent e–

direction of the arrow represents the spin of the electron.

• Standard Electron Configuration

• Condensed Electron Configurationuses the noble gases as a shortcut


Orbital Diagram for Hydrogen# e– = 1

Aufbau Principal!

WS Packet pg. 1


OrbitalDiagram for

Helium

# e– = 2

Pauli Exclusion Principal!


Orbital Diagram for

Lithium

# e– = 3


Orbital Diagram for

Beryllium

# e– = 4


Orbital Diagram for

Boron

# e– = 5


OrbitalDiagram for

Carbon# e– = 6

Hunds Rule!


Orbital Diagram for

Nitrogen

# e– = 7


Orbital Diagram for

Oxygen

# e– = 8


Electron Configurations

• Distribution of all e– in an atom

• Consist of… Number denoting

the principle energy level, n (also called an e– shell)



• Consist of …Letter denoting

the type of orbital (subshell)



• Consist of… Superscript

denoting the number of electrons in that orbital/subshell.


Standard Electron Configurations

• Oxygen, 8 e–

1s22s22p4

• Neon, 10 e–

1s22s22p6

notice that the 2nd energy level (shell) is completely full 2 s and 6 p = 8 e– (octet)

outer most energy level being full makes noble gases very stable


Condensed (Noble Gas) E.C.• Use the LAST noble gas that is located in the

periodic table right before the element.• Write the symbol of the noble gas in brackets.• Write the remaining configuration after the

brackets.Aluminum: 1s22s22p63s23p1 or [Ne] 3s23p1

• The noble gas represents the inner “core” e–

• The remaining configuration focuses on the valence e– in the outermost shell (energy level)


Valence Electron Trend - down a column -


Some Anomalies

• Some irregularities occur when there are enough e– to half-fill s and d orbitals on a given row.

• Ex) Chromium:

we would expect: [Ar] 4s2 3d4.

but really the E.C. is: [Ar] 4s1 3d5

• Because the 4s and 3d orbitals are very close in energy, an e– is moved from the s to the d orbital so that both are HALF-FULL

• Molybdenum and Tugsten behave the same way


Some Anomalies

• A similar instance occurs with copper• Ex) Copper:

we would expect: [Ar] 4s2 3d 9.

but really the E.C. is: [Ar] 4s1 3d10

• Because the 4s and 3d orbitals are very close in energy, an e– is moved from the s to the d orbital so that the s is HALF-FULL and the d is COMPLETELY FULL

• Silver and Gold behave the same way

chapter 6 electronic structure of atoms

Documents

type of radiant energy

color of light

smallest quantity of

electronicstructureof

light intensity

speed of light c

blackbody radiation

visible light vis