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Chemistry 101 : Chap. 6. 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

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Chemistry 101 : Chap. 6

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


Electronic Structure

 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


Wave Nature of Light

  • Electromagnetic Radiation :

    Visible lightis an example of electromagnetic radiation (EMR)

Electric Field

Magnetic Field


Wave Nature of Light

 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)


Wave Nature of Light

 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


Wave Nature of Light

Higher frequency

Longer wavelength


Wave Nature of Light

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

by the local radio station WHQR 91.3 MHz?


Wave Nature of Light

 Example : Calculate the frequency of radio wave emitted by a

cordless phone if the wavelength of EMR is 0.33m.


Physics in the late 1800’s

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


Black Body Radiation

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.


Black Body Radiation

“Ultraviolet catastrophe”

classical theory predicts

significantly higher intensity

at shorter wavelengths than

what is observed.

intensity

wavelength (nm)

visible region


Black Body Radiation

  • 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)


Quantization of Energy

 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 Js

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


Quantization of Energy

 Example : Calculate the energy contained in a quantum of EMR

with a frequency of 95.1 MHz.


Photoelectric Effect

 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-


Photoelectric Effect

  • 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.


EMR: Is it wave or particle?

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.


Continuous Spectrum

 Many light sources, including light bulb, produce light containing

many different wavelengths

continuous spectrum


Line Spectrum

 When gases are placed under low pressure and high voltage,

they produces light containing a few wavelengths.


Line Spectrum

 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)


Line Spectrum

 Example : Identify the locations of first three lines of hydrogen

line spectrum


Bohr Model of Hydrogen Atom

  • 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


Bohr Model of Hydrogen Atom

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 = 6

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 = 6

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 |


Bohr Model of Hydrogen Atom

 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?


Bohr Model of Hydrogen Atom

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?


Limitations of Bohr Model

  • 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.


The Wave Behavior of Matter

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)


The Wave Behavior of Matter

 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)


Quantum Mechanics

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)


Hydrogen Atom

in Quantum Mechanics

Probability to find a electron

  • The denser the stippling, the

  • higher the probability of finding

  • the electron


z

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


Bohr model vs.

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)


Bohr model vs.

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


Bohr model vs.

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


l =1

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


Magnetic Quantum Number

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


Quantum Numbers

 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


Atomic Orbitals

 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


Atomic Orbitals in H Atom

 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)


Atomic Orbitals

 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


Atomic Orbitals

3 dimensional representation of 1s, 2s, 3s orbitals

1s

2s

3s


Atomic Orbitals

3 dimensional representation of 2p orbitals


Atomic Orbitals

3 dimensional representation of 3d orbitals


Electron Spin Quantum Number

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

that characterizes electrons:

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


Many-Electron Atoms

 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)


Many-Electron Atoms

 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


Many-Electron Atoms

 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


Many-Electron Atoms

 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


Many-Electron Atoms

 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!


Many-Electron Atoms

 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


Many-Electron Atoms

 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


valence electrons (2)

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


coreelectrons =

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


Many-Electron Atoms

  • 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


[Ar]

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


1s

2p

2s

3p

3d

3s

4p

4s

4f

Electronic Structure of Atoms


Electronic Structure of Ions

 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


Electronic Structure of Ions

 Electron configurations of 11Na ion :

Valence Electrons

3

d

2

p

1

“coreelectrons” = [Ne]

s

11Na :

[Ne]

3s1

11Na+ :

[Ne]


coreelectrons = [Ar]

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]


Electronic Structure of Ions

 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


Electronic Structure of Ions

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

21Sc:

[Ar]

21Sc3+ : [Ar]

4s23d1

4

f

3

d

2

p

1

s


Electronic Structure of Ions

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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