Quantum Chemistry (REAL) Part 1A for October 19

Unit IV: Quantum Mechanics and Bonding

Light

• Before 1900, scientists thought that light behaved only as wave

• discovered that also has particle-like characteristics

Light as a Wave

• electromagnetic radiation: – form of energy that acts as a wave as it travels– includes: visible light, X rays, ultraviolet and

infrared light, microwaves, and radio waves

• All forms are combined to form electromagnetic spectrum

Light as a Wave

Light as a Wave• all form of EM radiation travel at a speed of 3.0

x 108 m/s in a vacuum• it has a repetitive motion• wavelength: (λ) distance between points on

adjacent waves; in nm (109nm = 1m)• frequency: (ν) number of waves that passes a

point in a second, in waves/second

Inversely proportional!c

Photoelectric Effect

• when light is shone on a piece of metal, electrons can be emitted

• no electrons were emitted if the light’s frequency was below a certain value

• scientists could not explain this with their classical theories of light

• Ex: coin-operated sift drink machine

Photoelectric Effect

• Max Planck: a German physicist• suggested that an object emits energy in the

form of small packets of energy called quanta• quantum- the minimum amount of energy that

can be gained or lost by an atom

Planck’s constant (h): 6.626 x 10-34 J*shE

Photoelectric Effect

• Einstein added on to Planck’s theory in 1905• suggested that light can be viewed as stream

of particles• photon- particle of EM radiation having no

mass and carrying one quantum of energy• energy of photon depends on frequency

Photoelectric Effect• EM radiation can only be absorbed by matter

in whole numbers of photons• when metal is hit by light, an electron must

absorb a certain minimum amount of energy to knock the electron loose

• this minimum energy is created by a minimum frequency

• since electrons in different metal atoms are bound more or less tightly, then they require more or less energy

H Line-Emission Spectrum

• ground state- lowest energy state of an atom• excited state- when an atom has higher

potential energy than it has at ground state• line-emission spectrum- series of wavelengths

of light created when visible portion of light from excited atoms is shined through a prism

H Line-Emission Spectrum• scientists using classical theory expected atoms

to be excited by whatever energy they absorbed• continuous spectrum- emission of continuous

range of frequencies of EM radiation

H Line-Emission Spectrum

• Why had hydrogen atoms only given off specific frequencies of light?current Quantum Theory attempts to explain this using a new theory of atom

H Line-Emission Spectrum

• when an excited atom falls back to ground state, it emits photon of radiation

• the photon is equal to the difference in energy of the original and final states of atom

• since only certain frequencies are emitted, the differences between the states must be constant

Bohr Model

• created by Niels Bohr (Danish physicist)in 1913

• linked atom’s electron with emission spectrum• electron can circle nucleus in certain paths, in

which it has a certain amount of energy

Bohr Model

• Can gain energy by moving to a higher rung on ladder

• Can lose energy by moving to lower rung on ladder

• Cannot gain or lose while on same rung of ladder

Bohr Model

a photon is released that has an energy equal to the difference between the initial and final energy orbits

Bohr Model

• problems:–did not work for other atoms–did not explain chemical behavior of atoms

Introduction to Quantum Theory

• Quantum Theory- describes mathematically the wave properties of electrons

Electrons as Waves• In 1924, Louis de Broglie

(French scientist)• suggested the way quantized

electrons orbit the nucleus is similar to behavior of wave

• electrons can be seen as waves confined to the space around a nucleus

• waves could only be certain frequencies since electrons can only have certain amounts of energy

Electrons as Waves

hvE

vc c

v

hc

E

2mcE 2mc

hc

vm

h

shows that anything with both mass and velocity has a corresponding wavelength

Uncertainty Principle

• In 1927 by Werner Heisenberg (German theoretical physicist)

• electrons can only be detected by their interaction with photons

• any attempt to locate a specific electron with a photon knocks the electron off course

• Heisenberg Uncertainty Principle- it is impossible to know both the position and velocity of an electron

Schrödinger Wave Equation

• In 1926, Erwin Schrödinger (Austrian physicist)

• his equation proved that electron energies are quantized

• only waves of specific energies provided solutions to his equation

• solutions to his equation are called wave functions

Schrödinger Wave Equation

• wave functions give only the probability of finding an electron in a certain location

• orbital- 3D area around a nucleus that has a high probability of containing an electron

• orbitals have different shapes and sizes

Quantum Numbers

• specify the properties of atomic orbitals and of electrons in orbitals

• the first three numbers come from the Schrödinger equation and describe:– main energy level– shape– orientation

• 4th describes state of electron

1st Quantum NumberPrincipal Quantum Number: n• main energy level occupied by electron• values are all positive integers (1,2,3,…)• As n increases, the electron’s energy and its

average distance from the nucleus increase• multiple electrons are in each level so have

the same n value• the total number of orbitals in a level is equal

to n2

1st Quantum Number

Energy

2nd Quantum Number

Angular Momentum Quantum Number: l• indicates the shape of the orbital (sublevel)• the possible values of l are 0 to n-1• each atomic orbital is designated by the principal

quantum number followed by the letter of the sublevel

2nd Quantum Number

s orbitals:• spherical • l value of 0• Max 2 electronsd

2nd Quantum Number

p orbitals:• dumbbell-shaped• l value of 1• Max. 6 electrons

2nd Quantum Number

d orbitals:• various shapes• l value of 2• Max. 10 electrons

2nd Quantum Number

f orbitals:• various shapes• l value of 3• Max. 14 electrons

2nd Quantum Number

Level Sublevels Sublevels

0 1 2 3

0 1 2

0 1

0

3rd Quantum Number

Magnetic Quantum Number: ml

• indicates the orientation of an orbital around the nucleus

• has values from -l +l• specifies the exact orbital that the electron is

contained in• each orbital holds maximum of 2 electrons

Energy Energy LevelLevel

(n)(n)

SublevelSublevels in Levels in Level

# # Orbitals Orbitals

in in SublevelSublevel

Total # Total # of of

Orbitals Orbitals in Levelin Level

11 l=0, sl=0, s 11 11

22 l=0, sl=0, s 11 44

l=1, pl=1, p 33

33 l=0, sl=0, s 11 99

l=1, pl=1, p 33

l=2, dl=2, d 55

44 l=0, sl=0, s 11 1616

l=1, pl=1, p 33

l=2, dl=2, d 55

l=3, fl=3, f 77

4th Quantum Number

Spin Quantum Number: ms

• indicates the spin state of the electron• only 2 possible directions• only 2 possible values: -½ and +½• paired electrons must

have opposite spins

Energy Level 1

nn ll mmll mmss

11 00 00 -½,+½-½,+½

Energy Level 2

nn ll mmll mmss

22 00 00 -½,+½-½,+½

11 -1-1 -½,+½-½,+½

00 -½,+½-½,+½

+1+1 -½,+½-½,+½

Energy Level 3

nn ll mmll mmss

33 00 00 -½,+½-½,+½

11 -1-1 -½,+½-½,+½

00 -½,+½-½,+½

+1+1 -½,+½-½,+½

22 -2-2 -½,+½-½,+½

-1-1 -½,+½-½,+½

00 -½,+½-½,+½

+1+1 -½,+½-½,+½

+2+2 -½,+½-½,+½

Energy Level 4nn ll mmll mmss

44 00 00 -½,+½-½,+½

11 -1-1 -½,+½-½,+½

00 -½,+½-½,+½

+1+1 -½,+½-½,+½

22 -2-2 -½,+½-½,+½

-1-1 -½,+½-½,+½

00 -½,+½-½,+½

+1+1 -½,+½-½,+½

+2+2 -½,+½-½,+½

ll mmll mmss

33 -3-3 -½,+½-½,+½

-2-2 -½,+½-½,+½

-1-1 -½,+½-½,+½

00 -½,+½-½,+½

+1+1 -½,+½-½,+½

+2+2 -½,+½-½,+½

+3+3 -½,+½-½,+½

Homework1. Give the values of n, ℓ, mℓ

and ms for every orbital

with n = 6. 2. Indicate whether the set of quantum numbers (n, ℓ,

mℓ) exits or not.

a. 1, 1, 0 e. 8, 1, 0 b. 5, 4, –3 f. –2, 1, +1c. 3, 2, –3 g. 4, 2, –1d. 6, 7, +7 h. 7, 3, +4

3. Draw the shapes (including the orientation) of all the s, p and d orbitals.

Homework4. Which orbital in each of the following pairs is higher in

energy? a. 5s or 5d b. 4s or 3p c. 6s or 4d

5. What is the maximum number of electrons in an atom that can have these quantum numbers? a) n = 2b) n = 3, c) n = 3, l = 1d) n = 4, l = 2 e) n = 5, l= 3, ml=3