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Electronic Structure of Atoms

- The Wave Nature of Light
- Quantized Energy and Photon
- (3) Line Spectra and Bohr Models
- (4) The Wave Behavior of Matter
- (5) Quantum Mechanics and Atomic Orbitals
- (6) Representations of Orbitals
- (7) Many Electron Atoms
- (8) Electron Configurations
- (9) Electron Configurations and Periodic Table

What is the electronic structure?

The way electrons are arranged in an atom

How can we find out the electronic structure experimentally ?

Analyze the light absorbed and emitted by substances

Is there a theory that explains the electronic structure of atoms?

Yes. We need “quantum mechanics” to explain the results

from experiments

- Electromagnetic Radiation :

Visible lightis an example of electromagnetic radiation (EMR)

Electric Field

Magnetic Field

Properties of EMR

All EMR have wavelike characteristics

Wave is characterized by its wavelength, amplitude and

frequency

EMR propagates through vacuum at a speed of 3.00 108 m/s

(= speed of light = c)

Frequency () and wavelength ()

Frequency measures how many wavelengths pass through a point per second:

4 complete cycles pass

through the origin

= 4 s-1 = 4 Hz

Note that the unit of is m

= c

1 s

Example : What is the wavelength, in m, of radio wave transmitted

by the local radio station WHQR 91.3 MHz?

Example : Calculate the frequency of radio wave emitted by a

cordless phone if the wavelength of EMR is 0.33m.

Universe

Matter (particles)

Wave (radiation)

F = ma

Newton’s equation

Maxwell’s equation

James C. Maxwell (1831-1879)

Isaac Newton (1643-1727)

The Failure of Classical Theories

In the late 1800, there were three important phenomena that

could not be explained by the classical theories

Black body radiation

Photoelectric effect

Line Spectra of atoms

Hot objects emit light.

The higher the temperature, the higher the emitted frequency

- Black body :

An object that absorbs all electromagnetic radiations that falls

onto it. No radiation passes through it and none is reflected.

The amount and wavelength of electromagnetic radiation

a black body emits is directly related to their temperature.

“Ultraviolet catastrophe”

classical theory predicts

significantly higher intensity

at shorter wavelengths than

what is observed.

intensity

wavelength (nm)

visible region

- Classical Theory :

Electromagnetic radiation has only wavelike characters.

- Energy (or EMR) can be absorbed and emitted in any amount.

Planck’s Solution :

He found that if he assumed that energy

could only be absorbed and emitted in

discrete amounts then the theoretical and

experimental results agree.

Max Planck (1858 - 1947)

Energy Quanta : Planck gave the name ``quanta’’ to the smallest

quantity of energy that can be absorbed or emitted as EMR.

E = h

Energy of a quantum

of EMR with frequency

frequency of EMR

h = Planck Constant

= 6.626 10-34 Js

NOTE : Energy of EMR is related to frequency, not intensity

NOTE : When energy is absorbed or emitted as EMR with

a frequency , the amount of energy should be a

integer multiple of h

Example : Calculate the energy contained in a quantum of EMR

with a frequency of 95.1 MHz.

Photoelectric Effect : When light of certain frequency strikes a

metal surface electrons are ejected. The velocity of ejected

electrons depend on the frequency of light, not intensity.

K.E.of ejected electron =

Energy of EMR Energy needed to release an e-

e-

Light of a certain minimum frequency

is required to dislodge electrons from

metals

e-

e-

e-

- Einstein’s Solution: In 1905, Einstein explained photoelectric

effect by assuming that EMR can behave as a stream of particles,

which he called photon. The energy of each photon is given by

Ephoton = h

K.E.e = h

incident

photon energy

binding energy

Kinetic energy

of ejected electrons

e-

e-

e-

Einstein’s discovery confirmed Planck’s

notion that energy is quantized.

Energy, Frequency and Wavelength

- Example : Calculate the energy of a photon of EMR with a

wavelength of 2.00 m.

Einstein’s theory of light poses a dilemma:

Is light a wave or does it consist of particles?

When conducting experiments with EMR using wave measuring

equipment (like diffraction), EMR appear to be wave

When conducting experiments with EMR using particle techniques

(like photoelectric effect), EMR appear to be a stream of particles

EMR actually has both wavelike and particle-like characteristics.

It exhibits different properties depending on the methods used

to measure it.

Many light sources, including light bulb, produce light containing

many different wavelengths

continuous spectrum

When gases are placed under low pressure and high voltage,

they produces light containing a few wavelengths.

Rydberg equation: The positions of all line spectrum () can be

represented by a simple equation.

RH (Rydberg Constant) = 1.096776 107 m-1 (for hydrogen)

n1 and n2 are integer numbers (n1 < n2)

- The electron is permitted to be in orbits of certain radii,
- corresponding to certain definite energies.

(2) When the electron is in such permitted orbits, it does not

radiate and therefore it will not spiral into the nucleus.

(3) Energy is emitted or absorbed by the electron only as the

electron changes from one allowed state (or orbit) to another.

This energy is emitted or absorbed as a photon, E=h

principal quantum number

ground state

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

excited states

nucleus

Bohr model proposed in 1913

Niels Bohr (1885 – 1962)

n = 5

n = 4

n = 3

n = 2

n = 1

Bohr Model of Hydrogen Atom

Question #1 : What is the energy of electron associated with each orbit?

n = 5

n = 4

n = 3

n = 2

n = 1

Bohr Model of Hydrogen Atom

Question #2 : How much energy will be absorbed or emitted when the

electron changes it orbit between n1 and n3?

n1 n3 : Einit < Efinal absorption

n3 n1 : Einit > Efinal emission

Energy

e

e

Ground State

Ground State

h = | Einit - Efinal |

Example : How much energy will be absorbed or emitted for

an electron transition from n=1 to n=3 ? What is the

frequency of light associated with such transition?

Is this result consistent with the Rydberg equation?

Energy gap decreases as n increases

Balmer series

Why the hydrogen line spectra (above)

shows only Balmer series, involving n=2?

What happens to the transitions

involving n=1?

What is the meaning of n = and E = 0?

- Bohr model does not work for atoms with more than
- one electron

Check out http://jersey.uoregon.edu/vlab/elements/Elements.html

for emission and absorption spectra all elements in periodic table

(2) There are more lines buried under the line spectrum of

hydrogen. Bohr model of hydrogen can not explain such

fine structure of hydrogen atom, which was discovered later.

Electrons in Bohr model are treated as particles. In order to

explain the electronic structure of atom, we need to incorporate

the wave-like nature of electron into the theory.

For a particle of mass m, moving with a velocity v,

De Broglie Wavelength

Louis de Broglie (1892-1987)

Example : What is the wavelength of an electron traveling at 1% of the

speed of light? Repeat the calculation for a baseball moving at 10 m/s.

(mass of electron = 9.11 10-31 kg, mass of baseball = 145 g)

Schrodinger developed a theory incorporating wave-like nature of particles

(1) The motions of particles can be described by wavefunction, (r).

(2) Wavefunction, (r), can tell us only the probability to locate

the particle at the position r

Schrodinger

equation

Werner Heisenberg (1901-1976)

Erwin Schrodinger (1887-1961)

in Quantum Mechanics

Probability to find a electron

- The denser the stippling, the
- higher the probability of finding
- the electron

y

x

Bohr model vs.

Quantum Mechanics

Bohr’s model:

n = 1

orbit

electron circles around nucleus

Quantum Mechanics:

orbital

n = 1

or

electron is somewhere

within that spherical region

Quantum Mechanics

Probability to find the electron at a distance r from the nucleus

(green = Bohr model, Red = Quantum Mechanics)

n = 1

n = 2

distance from nucleus (10-10 m)

distance from nucleus (10-10 m)

Quantum Mechanics

Bohr’s model:

requires only the principal quantum number (n) to describe an orbit

Quantum Mechanics:

needs three different quantum numbers to describe an orbital

n : principal quantum number

l : azimuthal quantum number

ml : magnetic quantum number

Quantum Mechanics

Energy level diagam

Quantum Mechanics

Bohr model

n=3

l = 2

Energy

n=2

l = 1

n=1

l = 0

Energy of electron in a given orbital :

Principal Quantum Number

Principal quantum number, n, in quantum mechanicsis

analogous to the principal quantum number in Bohr model

n describes the general size of orbital and energy

The higher n, the higher the energy of the electron

n is always a positive integer: 1, 2, 3, 4 ….

l is normally listed as a letter:

Value of l: 0 1 2 3

letter: spdf

Azimuthal Quantum Number

l takes integer values from 0 to n-1

e.g.

l= 0, 1, 2

for n = 3

l defines the shape of an electron orbital

p-orbital

(1 of 3)

l= 2

d-orbital

(1 of 5)

l = 3

f-orbital

(1 of 7)

Azimuthal Quantum Number

z

y

x

l = 0

s-orbital

ml takes integral values from -l to +l, including 0

ml= -2, -1, 0, 1, 2

e.g.

forl = 2

ml describes the orientation of an electron orbital in space

2Py

2Px

2Pz

Example : Which of the following combinations of quantum

numbers is possible?

n=1, l=1, ml= -1

n=3, l=0, ml= -1

n=3, l=2, ml= 1

n=2, l=1, ml= -2

Shell:

A set of orbitalswith the same principal quantum number, n

Total number of orbitals in a shell is n2

Subshells:

Orbitals of one type(same l)within the same shell

A shell of quantum number n has n subshells

n=3 shell : It has 3 subshells (3s,3p,3d)

n=2 shell : It has 2 subshells (2s, 2p)

There are 5 orbitals

in this subshell

Each orbital in this subshell has

the same n and l quantum number,

but different ml quantum number

n=1 shell : It has 1 subshell (1s)

Example: Fill in the blanks in the following table

Principal quantum Type of orbitals Total Number

Number (n) (subshell) of orbitals

1

2

3

4

3 dimensional representation of 2p orbitals

3 dimensional representation of 3d orbitals

Spin magnetic quantum number (ms) : A fourth quantum number

that characterizes electrons:

ms can only take two values, +1/2 or -1/2

For the same type of orbitals (i.e samel),

the energy of an orbital increases with n.

For a given value of n, the energy of an

orbital increases with l.

Orbitals in a given subshell (same n, l)

have the same energy (degenerate)

Aufbau Principle helps you to remember the order of energy levels

1s

2s 2p

3s 3p 3d

4s 4p 4d 4f

5s 5p 5d 5f

6s 6p 6d 6f

7s 7p 7d 7f

Electron configuration: The way in which electrons are distributed

among the various orbitals of an atom

(1) The orbitals are filled in order of increasing energy

(2) Pauli exclusion principle : No two electrons in an atom can have

the same set of four quantum numbers (n, l, ml, ms)

Maximum 2 electrons can occupy a single orbital. These two

electrons have the same (n, l, ml) quantum numbers, but different

msquantum number: one has ms = +1/2 (spin-up) and the other has

ms= -1/2 (spin-down)

or 1s2

or

1s

1s

Electron configurations of H, He, Li, Be, B

1s1

H :

1s

2s

2p

1s2

He :

1s

2s

2p

1s22s1

Li :

1s

2s

2p

1s22s2

Be :

1s

2s

2p

B :

1s22s22p1

1s

2s

2p

Electron configuration of C :

Or

1s

2s

2p

1s

2s

2p

Which configuration has the lower energy?

(3) Hund’s Rule : For degenerate orbitals, the lowest energy is attained

when the number of electrons with the same spin is maximized.

Sum of ms value has to be maximized

Total ms value = +1/2 – 1/2 = 0

Total ms value = +1/2 + 1/2 = 1

Lower Energy!

Electron configurations of C, N, O, F, N

1s22s22p2

C :

1s

2s

2p

1s22s22p3

N :

1s

2s

2p

1s22s22p4

O:

1s

2s

2p

1s22s22p5

F :

1s

2s

2p

1s22s22p6

Ne :

1s

2s

2p

Electron configurations of 14Si

Valence Electrons

orbital diagram

(no energy info)

3

d

2

p

1

“coreelectrons”

s

14Si

1s22s22p63s23p2

Line notation

[Ne]

Condensed line notation

3s23p2

coreelectrons =

electron configuration

of the preceding noble gas

Many-Electron Atoms

- Example :What is the electronic structure of Ca? Which electrons

are core electrons and which are valence electrons?

[Ar]

4s2

20Ca :

(4s orbital is filled before 3d !)

4

f

3

d

2

p

1

s

electron configuration

of the preceding noble gas

Many-Electron Atoms

- Example :What is the electronic structure of Br? Which electrons

are core electrons and which are valence electrons?

[Ar]

3d104s24p5

35Br :

(4s orbital is filled before 3d !)

valence electrons (7)

4

f

3

For main group elements,

electrons in a filled d-shell

(or f-shell) are not valence

electrons

d

2

p

1

s

- Example :What is the electronic structure of V? Which electrons

are core electrons and which are valence electrons?

[Ar]

3d34s2

23V:

(4s orbital is filled before 3d !)

4

f

3

d

2

valence electrons (5)

p

1

coreelectron =

electron configuration

of the preceding noble gas

s

3d44s2

is less stable than

[Ar]

3d54s1

Many-Electron Atoms

- Example :What is the electronic structure of Cr? Which electrons

are core electrons and which are valence electrons?

[Ar]

3d54s1

24Cr:

4

f

3

d

2

p

1

s

A half-filled or completely filled d-shell is a preferred configuration

Atoms form ions in order to achieve more stable electron

configurations

Metals : ALWAYS LOSE electrons to become

positive ions (cation)

Non-metals: USUALLY GAIN electrons to become

negative ions (anion)

Generally, atoms form ions by loosing or gaining electrons

to achieve the electron configuration of nearest noble gas

Electron configurations of 11Na ion :

Valence Electrons

3

d

2

p

1

“coreelectrons” = [Ne]

s

11Na :

[Ne]

3s1

11Na+ :

[Ne]

Electronic Structure of Ions

Electron configurations of 35Br ion :

valence electrons (7)

4

f

3

d

2

p

1

s

[Ar]

3d104s24p5

35Br :

35Br :

[Ar]

3d104s24p6

= [Kr]

Example : What is the electron configuration of Fe and the ions

formed by Fe?

26Fe:

[Ar]

26Fe2+ : [Ar]3d6

26Fe3+ : [Ar]3d5

4s23d6

4

f

3

d

2

p

1

s

4s electrons (higher n) are removed before 3d electrons

Example : What is the electron configuration of ion formed by Sc?

21Sc:

[Ar]

21Sc3+ : [Ar]

4s23d1

4

f

3

d

2

p

1

s

Isoelectronic = Same electron configuration

37Rb+ :

[Ar]

3d104s24p6

= [Kr]

35Br- :

[Ar]

3d104s24p6

= [Kr]

34Se2- :

[Ar]

3d104s24p6

= [Kr]

37Rb+, 35Br -, 34Se2- are isoelectronic !

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