chemistry 101 : chap. 6 electronic structure of atoms (1) the wave nature of light (2) quantized...

Chemistry 101 : Chap. 6Chemistry 101 : Chap. 6

Electronic Structure of Atoms

(1) The Wave Nature of Light

(2) 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 StructureElectronic 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 LightWave Nature of Light

Electromagnetic Radiation :

Visible light is 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:

1 s

4 complete cycles pass

through the origin

= 4 s-1 = 4 Hz

Note that the unit of is m

= c


Higher frequencyLonger wavelength


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.

Physics in the late 1800’sPhysics in the late 1800’s

Universe

Matter (particles) Wave (radiation)

F = ma

Newton’s equation

Isaac Newton (1643-1727)

0

BJt

EB

Et

BE

Maxwell’s equation

James C. Maxwell (1831-1879)

The Failure of Classical TheoriesThe 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 RadiationBlack Body Radiation

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.

Hot objects emit light.

The higher the temperature, the higher the emitted frequency


wavelength (nm)

inte

nsity

visible region

“Ultraviolet catastrophe” classical theory predictssignificantly higher intensityat shorter wavelengths thanwhat is observed.


Classical Theory :

Electromagnetic radiation has only wavelike characters.

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

Planck’s Solution :

Max Planck (1858 - 1947)

He found that if he assumed that energy

could only be absorbed and emitted in

discrete amounts then the theoretical and

experimental results agree.

1exp

8)(

5

kThc

hcI

Quantization of EnergyQuantization 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

h = Planck Constant = 6.626 10-34 Js

Energy of a quantumof EMR with frequency

frequency of EMR

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 EnergyQuantization of Energy

Example : Calculate the energy contained in a quantum of EMR

with a frequency of 95.1 MHz.

Photoelectric EffectPhotoelectric 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.

e- e- e-

e-

K.E.of ejected electron =

Energy of EMR Energy needed to release an e-

Light of a certain minimum frequency

is required to dislodge electrons from

metals

Photoelectric EffectPhotoelectric 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

e- e- e-

K.E.e = h

incident photon energy

binding energy Kinetic energyof ejected electrons

Einstein’s discovery confirmed Planck’snotion that energy is quantized.

Energy, Frequency and Wavelength

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?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 SpectrumContinuous Spectrum

Many light sources, including light bulb, produce light containing many different wavelengths

continuous spectrum

Line SpectrumLine 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.

22

21

111

nnRH

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

n1 and n2 are integer numbers (n1 < n2)


Example : Identify the locations of first three lines of hydrogen

line spectrum

Bohr Model of Hydrogen AtomBohr Model of Hydrogen Atom

(1) 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


n = 1n = 2n = 3n = 4n = 5n = 6

nucleus

Bohr model proposed in 1913Niels Bohr (1885 – 1962)

principal quantum number

ground state

excited states


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

218

2

1)1018.2(

1)(

nJ

nhcRE H

n = 6n = 5n = 4

n = 3

n = 2

n = 1

4

11018.2 18 JE

JE 181018.2

9

11018.2 18 JE

n = 6n = 5n = 4

n = 3

n = 2

n = 1

Energy

Ground State

e

Ground State e


h = | Einit - Efinal |

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

electron changes it orbit between n1 and n3?

n3 n1 : Einit > Efinal emission n1 n3 : Einit < Efinal absorption


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?


Why the hydrogen line spectra (above)

shows only Balmer series, involving n=2?

What happens to the transitions

involving n=1?

Balmer series

Energy gap decreases as n increases

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

Limitations of Bohr ModelLimitations of Bohr Model

(1) Bohr model does not work for atoms with more than

one electron

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

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

The Wave Behavior of Matter 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.

Louis de Broglie (1892-1987)

vm

hDe Broglie Wavelength

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

The Wave Behavior of Matter 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 MechanicsQuantum 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

Erwin Schrodinger (1887-1961)

Schrodingerequation

Werner Heisenberg (1901-1976)

Hydrogen Atom in Quantum Mechanics

Hydrogen Atom in Quantum Mechanics

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

Probability to find a electron

Bohr model vs. Quantum Mechanics


or

n = 1

n = 1

orbit

orbitalz

x

y

Bohr’s model:

Quantum Mechanics:

electron circles around nucleus

electron is somewherewithin that spherical region



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’s model:

Quantum Mechanics:

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

n : principal quantum numberl : azimuthal quantum numberml : magnetic quantum number

needs three different quantum numbers to describe an orbital



Energy level diagam

n=1

n=2

n=3

Energy

Bohr model Quantum Mechanics

l = 1

l = 0

l = 2

Principal Quantum NumberPrincipal Quantum Number

Principal quantum number, n, in quantum mechanics is

analogous to the principal quantum number in Bohr model

The higher n, the higher the energy of the electron

Energy of electron in a given orbital :

2

1n

RchE H

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

n describes the general size of orbital and energy

Azimuthal Quantum NumberAzimuthal Quantum Number

l takes integer values from 0 to n-1

for n = 3 l = 0, 1, 2e.g.

l is normally listed as a letter:

Value of l: 0 1 2 3 letter: s p d f

l defines the shape of an electron orbital

Azimuthal Quantum NumberAzimuthal Quantum Number

z

x

y

l = 0s-orbital

l =1p-orbital(1 of 3)

l = 2 d-orbital(1 of 5)

l = 3f-orbital(1 of 7)

Magnetic Quantum NumberMagnetic Quantum Number

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

for l = 2 ml = -2, -1, 0, 1, 2e.g.

ml describes the orientation of an electron orbital in space

2Pz2Px

2Py

Example : Which of the following combinations of quantum numbers is possible?

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

n=3, l=2, ml= 1

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

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

Quantum NumbersQuantum Numbers

Atomic OrbitalsAtomic Orbitals

Shell:

A set of orbitals with the same principal quantum number, n

Subshells:

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

A shell of quantum number n has n subshells

Total number of orbitals in a shell is n2

Atomic Orbitals in H AtomAtomic Orbitals in H Atom

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

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

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

There are 5 orbitals in this subshell

Each orbital in this subshell hasthe same n and l quantum number,but different ml quantum number


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 1s, 2s, 3s orbitals

1s 2s 3s


3 dimensional representation of 2p orbitals


3 dimensional representation of 3d orbitals

Electron Spin Quantum NumberElectron 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 AtomsMany-Electron Atoms

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

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

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

ms = -1/2 (spin-down)

1s

or

1s

or 1s2


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

H :

1s

He :

1s

Li :1s 2s

Be :

1s 2s

B :

1s 2s 2p

1s1

1s2

1s22s1

1s22s2

1s22s22p1

2s

2s

2p

2p

2p

2p


Electron configuration of C :

1s 2s 2p 1s 2s 2p

Or

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

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

Which configuration has the lower energy?

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

C :

N :

O:

F :

Ne :

1s 2s 2p

1s22s22p2

1s 2s 2p

1s22s22p3

1s 2s 2p

1s22s22p4

1s 2s 2p

1s22s22p5

1s 2s 2p

1s22s22p6


[Ne]

14Si 1s22s22p63s23p2 Line notation

orbital diagram(no energy info)

s

p

d

1

2

3

Condensed line notation

“core electrons”

3s23p2

Electron configurations of 14Si

Valence Electrons

Example : What is the electronic structure of Ca? Which electrons are core electrons and which are valence electrons?


valence electrons (2)

core electrons = electron configuration

of the preceding noble gas

s

p

d

1

2

3

20Ca : 4s2

4

f

(4s orbital is filled before 3d !)[Ar]


Example : What is the electronic structure of Br? Which electrons are core electrons and which are valence electrons?


core electrons = electron configuration


s

p

d

1

2

3

35Br : 3d104s24p5

4

f

(4s orbital is filled before 3d !)[Ar]

For main group elements,electrons in a filled d-shell(or f-shell) are not valenceelectrons


Example : What is the electronic structure of V? Which electrons are core electrons and which are valence electrons?

s

p

d

1

2

3

4

f

23V: [Ar] 3d34s2

core electron = electron configuration



(4s orbital is filled before 3d !)


Example : What is the electronic structure of Cr? Which electrons are core electrons and which are valence electrons?

s

p

d

1

2

3

4

f

24Cr: [Ar] 3d54s1

[Ar] 3d44s2 is less stable than [Ar] 3d54s1

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

1s

2s 2p

3s 3p

4s

3d

4p

4f

Electronic Structure of AtomsElectronic Structure of Atoms

Electronic Structure of IonsElectronic 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


Electron configurations of 11Na ion :

[Ne]11Na :

s

p

d

1

2

3

“core electrons” = [Ne]

3s1

Valence Electrons

[Ne]11Na+ :



core electrons = [Ar]s

p

d

1

2

3

35Br : 3d104s24p5

4

f

[Ar]

Electron configurations of 35Br ion :

35Br : 3d104s24p6 [Ar] = [Kr]


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

formed by Fe?

s

p

d

1

2

3

4

f

26Fe: [Ar] 4s23d6

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

26Fe2+ : [Ar]3d626Fe3+ : [Ar]3d5


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

s

p

d

1

2

3

4

f

21Sc: [Ar] 4s23d121Sc3+ : [Ar]


Isoelectronic = Same electron configuration

37Rb+ :

35Br- : [Ar] 3d104s24p6 = [Kr]

34Se2- : [Ar] 3d104s24p6 = [Kr]

[Ar] 3d104s24p6 = [Kr]

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

chemistry 101 : chap. 6 electronic structure of atoms (1) the wave nature of light (2) quantized...

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