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TOPIC VIII: Electronic Structure in Atoms

LECTURE SLIDES

Electromagnetic Radiation: E, , Early Models

Quantum Numbers

Shells, Subshells, Orbitals

Kotz & Treichel, Chapter 7

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WHERE THE ELECTRONS ARE.....

We are going to examine in historical succession

the ideas and experiments that led to the modern

atomic theory and sophisticated placement of theelectrons about the nucleus.

The current theory, based on quantum mechanics,

places the electrons around the nucleus of the atom

in ORBITALS, regions corresponding to allowed

energy states in which an electron has about 90%

probability of being found.

Lets see how we got there!

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Historical Events, Nature of

Electromagnetic Radiation1. 1864 James Maxwell: Wave motion of electromagnetic

radiation

2. 1885 Rydberg, Balmer: Wavelength of atomic spectra

3. 1900 Max Planck: Quantum theory of radiation, packets

of specific energy

4. ~1905 Einstein: Particle- like properties of radiation,

photons

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James Maxwell described all forms of radiation in

terms of oscillating (wave like) electricand magnetic

fields in space. The fields are propagated at right angles

to each other.

All forms of radiation include visible light but also,x-rays, radioactivity, microwaves, radio waves: all

are described today as electromagnetic radiation.

The waves have characteristic frequency and wavelength,and travel at a constant velocity in a vacuum,

3.0 X 10 8 m/s.

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wavelength

node

crest

trough

crest

trough

node

cycle

Wave description:

Frequency: # cycles / sec

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c =

speed light, vacuum = wavelength X frequency

3.00 X 108

ms-1

=, m X

, s

-1

(hertz)

hertz, Hz, s-1

# cycles per secondSame as m/s

= c/ = c/

Important Relationship, all electromagnetic radiation:

Rearranging:

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A red light source exhibits a wavelength of700 nm,

and a blue light source has a wavelength of400 nm.

What is the characteristic frequency of each of these

light sources?

Red light:

700 nm = ? m =? s-1

700 nm 1m = 700 X 10-9 m = 7.00 X 10-7m

109 nm

= c / = 3.00 X 108ms-1 = 4.29 X 1014 s-17.00 X 10-7 m

= 4.29 X 10

14

cycles per sec = 4.29 X 10

14

Hz or s

-1

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RED light: 700 nm, 4.29 X 1014 Hz

BLUE light: 400 nm, 7.50 X 1014Hz

Point to remember: theshorterthe wavelength, thehigherthe frequency: the longerthe wavelength,

the lowerthe frequency.

longer lowe

r

shorter higher

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GROUP WORK 8.1Microwave ovens sold in US give off microwave

radiation with a frequency of2.45 GHz. What is the

wavelength of this radiation, in m and in nm? = c/2.45 GHz = ? m = ? nm

109 Hz (s-1) = 1 GHz

c = 3.00 X 108 ms-1

1. Convert GHz to Hz; call Hz s-1

2. Calculate wavelength, , in m3.Convert m to nm (10

9

nm = 1 m)

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For one quantum of radiation:

Energy = h x radiation = h x cradiationhis Plancks constant, 6.63 X 10-34joulesec

Max Planck made a major step forward with his

theory that energy is not continuous but rather is

generated in small, measurable packets he called

quantum (which refers back to the Latin, meaningbundle).

He related the energy of the quantum to its frequency

orwavelength as below:

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Energy UnitsThe calorie: The quantity of energy required to raise1.00 g of water 1oC. Very small amount of energy, so

Kcal are generally used:

1000 calories(cal) = 1 kilocalorie, kcal

SI unit of energy is the joule, defined in terms of

kinetic energy rather than heat energy. One joule is the

amount of kinetic energy involved when a 2.0 kg object

is moving with a velocity of 1.0 m/s. Again, a very small

amount of energy, so kilojoules are generally used:

1000 joules (J) = 1 kilojoule kJ (kJ)

Relationship: 1 calorie = 4.184 joules

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Sample Calculations:

E = h =h c

Blue light, = 4.00 X 10-7 mE = 6.63 X 10-34 joule s x 3.00 X 108 ms-1

4.00 X 10-7 mE = 4.97 X 10-19 joule

Microwave oven, = 2.45 X 109 Hz or s-1E = 6.63 X 10-34 joule s x 2.45 X 109 s-1

E = 1.62 X 10-24 joule

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The relationships expressed by this equation

include the following:

Energy of a quantum is directly proportional to the

frequency of radiation: high frequency radiation is

the highest energy radiation (x rays, gamma rays)

Energy of radiation is inversely proportional to its

wavelength: long waves are lowest in energy, short

waves are highest. Radio waves, microwaves, radar

represent low energy forms of radiation.

View CD ROM sliding spectra here

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Group Work 8.2a: Rank radiation types by

increasing energy (#5 = highest)

microwave 2.36 cm

cosmic ()radiation 2.36 pm

Infraredradiation

2.36 m

X rayradiation

2.36 nm

FM radio 2.36 m

wavelength Energy rank

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Group Work 8.2b: Rank radiation types by

increasing energy (#5 = highest)

FM radio 89.7 MHz

Microwave 2.45 GHz

SubmarineRadio waves

76 Hz

Violet Light 7.3 X 10 s-

Orange Light 4.8 X 10 s-

frequency Energy rank

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Einsteintook the next step in line by using Plancks

quantum theory to explain the photoelectric effectin which high frequency radiation can cause electrons

to be removed from atoms.

Einstein decided that light has not only wave- like

properties typical of radiation but also particle- likeproperties. He renamed Plancks energy quantum as

a photon, a massless particle with the quantized

energy/frequency relationships described by Planck.

Quantized refers to properties which have specific

allowed values only.

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c, speed of light = Wavelength,

Xfrequency,

= c = c

Wavelength, frequency, energy relationships:

energy of photon = h, Plancks constant x E = h = h c

c = 3.00 X 108 ms-1, speed of light in vacuum

h = 6.63 X 10-34 joule s

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It was discovered in this time frame that each element

which was subjected to high voltage energy source

in the gas state would emit light.

When this light is passed through a prism, instead of

obtaining a continuous spectrum as one obtains for

white light, one observes only a few distinct lines of very

specific wavelength.

Each element emits when excited its own distinct line

emission spectrum with identifying wavelengths.

This important discovery lead directly to our modern

understanding of electronic structure in the atom!Checkout CD-ROM...

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Historical

Events, the Nature of Electron1. 1804 Dalton: Indivisible atom

2. 1897 Thomson: Discovery of electrons

3. 1904 Thomson: Plum Pudding atom

4. 1909 Rutherford: The Nuclear atom

5. 1913 Bohr:Planetary atom model, es in orbits

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The Plum Pudding Atom:

Positive matter with electrons embedded likeraisins in a pudding

JJ Thompsons Picture of the atom:

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TheRutherfordNuclearAtom:

Massandpositivechargeintinynucleusincenterofatoms;electronsdispersedoutsidenucleus

Rutherfords Picture of the Atom:

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Bohrcombined the ideas we have met to present

his planetary model of the atom, with the electrons

circling the nucleus like planets around the sun:

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Bohrused all the ideas to date:

electron in the atom outside the tiny positive nucleus

excited elements emit specific wavelengths of energy

only

radiation comes in packets of specific energy and

wavelength

Bohrs atom placed the electrons in energy quantized orbitsabout the nucleus and calculated exactly the energy of the

electron for hydrogen in each orbit.

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1

2

3

4

5

6

n, integer values for shells around nucleus, = 1-6-->infinity

n=1, lowest energy orbit n=6, highest energy orbit pictured

each orbit is quantized: has an energy of a specific frequency only

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allowed transitions shown by arrows: e may be "excited" to higher orbitonly if energized by photon of energy of matching frequency; it falls backto lower shell emitting the energy it has gained in form of light.

The wavelength of the light emitted represents the energy difference

between the orbits

2

3

4

left: e excited, photon ofcorrect, matching energy

right: e returning to origin,emitting light: line spectra

e

e

e

e

1

2

3

4

1

e

e

ee

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Bohr also predicted that each shell or orbit about the

nucleus would have its occupancy limited to 2n2

electrons, where n = the orbit number.

Many of Bohrs ideas, in modified form, remain in the

present day quantum mechanics description of atomic

structure.

Bohrwas able to calculate exactly the energy values forthe hydrogen spectrum using his model; however the

calculations only worked for one electron systems and

did not explain the electronic behavior of larger atoms.

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PlanckEnergy is quantized, comes in packets called quantum

with energy hv

Einstein

Energy can interact with matter, photoelectric effect,

quantum renamed photon

Bohr

Photons of energy can interact with electrons in orbits oflowest possible energy around the nucleus and excite

es to higher energy orbits. The es give off this energy

as light, spectral lines as they return to ground state.

Summation:

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Electron as matter/energy particle1. 1925 DeBroglie: Matter Waves

2. 1926 Heisenbergs Uncertainty Principle

3. 1926 Schroedingers Wave Equation and Wave

Mechanics

4. Modern Theory: Use of wave equation to describeelectron energy/probable location in terms of

three quantum numbers.

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DeBroglie next suggested that all mattermoved in

wavelike fashion, just like radiation. Largemacroscopic matter (moving golf balls, raindrops,

etc) have characteristic wavelengths associated

with their motion but the wavelengths are too tiny

to be detectable or significant.

Electrons, on the other hand have very significant

wavelengths in comparison to their size.

Einstein gave radiation matter- like, particle

properties; DeBroglie gave matter wave- like

properties.

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If an electron has some properties that are wave like

and others that are like particles, we cannot

simultaneously describe the exact location of the

electron and its exact energy. The accurate

determination of one changes the value of the other.

The Bohr atom tried to describe exact energy and

positionfor the es around the nucleus and worked

only for H.

Heisenbergs Uncertainty Principle:

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If we want to make an accurate statement about the

energy of an electron in the atom, we must accept

some uncertainty in its exact position. We can only

calculate probable locations where an electrons is to

be found.

Schroedingers wave equation describes the electron as

as a moving matter wave, and results in a picture inwhich we place electrons in probable locations about

the nucleus based on theirenergy.

Bornsinterpretation of Heisenbergs Uncertainty

Principle:

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Schroedingers Wave Equation

The mathematics employed by Schroedingerto describe

the energy and probable location of the electron aboutthe nucleus is complex and only recently been solved

for larger atoms than hydrogen.

However, it yields a description of the atom which

accounts for the differences between the elements.

IT WORKS!

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Schroedingers wave equation describes the

electrons in a given atom in terms ofprobable

regions ofdiffering energies in which an electronis most likely to be found.

We call the regions orbitals rather than

orbits, and each is centered about the nucleus.

The description of each orbital is given in the

form of three quantum numbers, which give

an address - like assignment to each orbital. The

quantum numbers are in the form of a series of

solutions to the wave equation.

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Group Work 8.4: Match

Scientist with Contribution

a) Bohr Energy of Quantum

b) Dalton Indivisible Atom

c) Einstein Nuclear Atom

d) Heisenberg Plum Pudding Atom

e) Planck Quantum to Photon

f) Rutherford Solar System Atom

g) Schroedinger Uncertainty Principle

h) Thompson Wave Equation

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The Quantum NumbersLocators, which describe each e- about the nucleus

in terms ofrelative energy and probable location.

The first quantum number, n, locates each electron

in a specific main shell about the nucleus.

The secondquantum number, l, locates the electron in a

subshell within the main shell.

The third quantum number, ml, locates the electron in

a specific orbital within the subshell.

QUANTUM NUMBERS

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n, the Principal quantum number:

Has all integervalues 1 to infinity: 1,2,3,4,...

Locates the electron in an orbital in a main shellabout the nucleus, like Bohrs orbits

describes maximum occupancy of shell, 2n2.

The higher the n number: the largerthe shell

the fartherfrom the nucleus

the higherthe energy of the orbital in the shell.

Locator #1, n, the first quantum number

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1

2

3

4

5

6

7

"n" MAIN SHELLS ABOUT THE NUCLEUS

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Locator #2, l, the second quantum number

limits number of subshells per shell to a value equal

to n:n =1, 1 subshell

n = 2, 2 subshells

n= 3, 3 subshells .....

only four types of subshells are found to be

occupied in unexcited, ground state of atom.

These subshell types are known by letter:

s p d f

locates electrons in a subshell region within themain shell

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n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

n = 7

1s

2s 2p

3s 3p 3d

4s 4p 4d 4f

5s 5p 5d 5f (5g)

6s 6p 6d (6f 6g 6h)

7s (7p 7d 7f 7g 7h 7i)

Lowest energy, smallest shell

Highest,

biggest

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Locator #3, ml,the third quantum number

ml, the third quantum number, specifies

in which orbital within a subshell an electron

may be found.

It turns out that each subshell type contains a unique

number of orbitals, all of the same shape and energy.

Main shell subshells orbitals

n# l#ml#

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The Third Q#, mlcontinued

ml values will describe the number oforbitals within asubshell, and give each orbital its own unique address:

ssubshel l psubshel l dsubshel l fsubshel l

1 orbital 3 orbitals 5 orbitals 7 orbitals

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dp p p

s

d d d d

f f f f f f ff

d

p

s

ml

l

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All electrons can be located in an orbital within a

subshell within a main shell. To find that electron one

need a locating value for each:

the n number describes a shell

(1,2,3...)

the l number describes a subshell region

(s,p,d,f...)the ml number describes an orbital within the

region

(Each of these quantum numbers has a series of

numerical values. We will only use the n numerical

values, 1-7.)

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Group Work 8.5Shell n# Name

AllowedSubshells

TotalOrbitalsAvailable

#1

#2

#3

#4

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It was subsequently discovered that each orbital

we have described is home to not just one but two

electrons, with opposite spins!

We are now treating an electron as a spinning chargedmatter particle, rotating clockwise or counterclockwise

on its axis: (next slide)

To describe this situation, a fourth quantum numberis required, the magnetic quantum number, ms.

The 4th Quantum Number, ms

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As a consequence, we now know:

ssubshell, one orbital,2 espsubshell, three orbitals,6 es,

d subshell, five orbitals, 10 es,

f subshell, seven orbitals, 14es,

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This 4th Q#completes the set of descriptors or

locators needed to assign each electron a unique

position in the arrangement around the nucleus.

Paulis Exclusion Principlesums it up: no two es in the

same atom, can have the same four Q#s. .

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f

d

p

s

ml

lms

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n = 1

n = 2

n = 3

n = 4

s p d f

2es 6 es 10 es 14 es

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Group Work 8.6: Number of Electrons per Shell

Shells Name,

Allowed

Subshells

Total Number,

Allowed

Orbitals

Total

Number,

Electrons

#1 1s 1

#2 2s, 2p 1 + 3 =4

#3 3s, 3p, 3d 1 + 3 + 5 = 9

#4 4s, 4p, 4d, 4f 1 + 3 + 5 + 7 =16

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Now that we have found places to put our electrons,

in orbitals within subshells within shells, lets take alook at the shapes of the various types of orbitals.

The orbital shapes are simply enclosed areas of

probability for an electron after a three dimensional

plot is made of all solutions for that electron from thewave equation.

Each orbital within a subshell is centered about the

nucleus and extends out to the boundaries of itsmain shell. Its exact orientation within the subshell

depends on the value of its mlnumber.

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all s orbitals

all p orbitals

d orbitals

Checkout CD-ROM!

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Energy Description of esThe first two quantum numbers, n and l, give

information about the relative energy of electrons

in their location:

As the n number increases, the energy of the e

in that shell increases: 1

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The ml number describes the numberof orbitals

within a subshell of the same energy.

Accordingly, the relative energy of an electron in

any given orbital within a subshell is given by the

sum of its n and l numbers.

We have described the following subshells for the

electrons:

1s; 2s, 2p; 3s, 3p, 3d; 4s, 4p, 4d, 4f; 5s, 5p, 5d, 5f;

6s, 6p, 6 d;7s

Lets next discuss their relative energy...

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Relative energy of subshells

n = 7 7

n = 6 6 7 8

n = 5 5 6 7 8n = 4 4 5 6 7

n = 3 3 4 5

n = 2 2 3

n = 1 1

s p d f

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Order of Filling, Lowest energy to Highest

n = 7 7

n = 6 6 7 8

n = 5 5 6 7 8n = 4 4 5 6 7

n = 3 3 4 5

n = 2 2 3

n = 1 1

s p d f

START HERE

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Periodic Table as GuideThe periodic table lists all elements sequentially in order

of atomic number: this means that each element in turn

has one more electron than its predecessor.

Well call this electron, the last one to be placed around

the nucleus, the distinguishingelectron...

We can subdivide the PT into four blocks, showing which

elements have theirdistinguishing or final electron

in an s or a p or a d or a f type subshell.

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Subshells by order of filling,

Lowest energy to highest1s 1s

2s 2s 2p 2p 2p 2p 2p 2p

3s 3s 3p 3p 3p 3p 3p 3p

4s 4s 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 4p 4p 4p 4p 4p 4p

5s 5s 4d 4d 4d 4d 4d 4d 4d 4d 4d 4d 5p 5p 5p 5p 5p 5p

6s 6s 5d 4f 5d 5d 5d 5d 5d 5d 5d 5d 5d 6p 6p 6p 6p 6p 6p

7s 7s 6d 5f 6d 6d 6d 6d 6d 6d

Where the Final Electron Goes:

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Where the Final Electron Goes:

s,f,d,p Blocks of Elements

s

fd

p

2 es14 es

10 es 6 es

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Our next task is to fill electrons around the nucleus into

the orbitals we have described. The electrons will fillfrom lowest energy subshell to highest.

The sum ofn + lgives us a ranking order of filling

subshells which does not simply progress fromcompletion of one shell to beginning of another.

However, We will use the periodic table to guide us

quickly through this complex sequence order.

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Group Work 8.7: Order of Subshell Filling By PT

1st

Period

2

nd

Period

3rd

Period

4th

Period

5th

Period

6th

Period

7th

Period

Name subshell s f d p