chemistry 161 chapter 8 quantum mechanics 1. structure of an atom subatomic particles electrons...

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CHEMISTRY 161 Chapter 8 Quantum Mechanics

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CHEMISTRY 161

Chapter 8

Quantum Mechanics

1. Structure of an Atom

subatomic particles

electrons

protons neutrons

17p18n

17e

3517Cl

mass number

atomic number

18 neutrons

e-

classical physics predicts that electron

falls into nucleus

Why are atoms stable?

2. Waves

EXP1

Inte

nsi

ty

distance, x

. .direction of propagation

wavelength [m]amplitude

v = x/t t = x/v

Inte

nsi

ty

time, t

. .direction of propagation

period [s]

T

T1Frequency [s-1]

[1 Hz = 1 s-1]

Hertz

Frequency and Wavelength

= c

wavelength frequency speed of radiationmeter (m) Hz or s-1 m s-1

LONG WAVELENGTH, LOW FREQUENCY

light can be described as a wave

James Maxwell

POSTULATE

visible light consist of

electromagnetic waves

speed of propagation

(speed of light)

c = 3 108 ms-1

light has two components

1.electric field

2.magnetic field

ELECTROMAGNETIC SPECTRUM

INCREASING FREQUENCY & ENERGY

Which color has the higher frequency?

1 = orange 2 = blue

= c

Wavelength (nanometers)

VISIBLE SPECTRUM

The wavelength of the yellow light from a lamp is 589 nm.

What is the frequency of the radiation?

c

7589 5.89 10nm m

1147

18

1009.51089.510998.2

s

mmsc

Li Na K

different atoms emit distinct lightEXP2

3. Postulates

E h

Max Planck

h is Planck’s constanth = 6.626 x 10-34 J s

energy can be emitted or absorbed only in discrete quantities (little packages)

EXP3/4

Emission Nebula

E h

CLASSICAL

any amount of energy can be emitted or absorbed

NON-CLASSICAL

energy can be emitted or absorbed only in discrete quantities (little packages)

E n h energy is not continuous

QUANTUM

smallest amount of energy which can be absorbed/ emitted

Albert Einstein

Electromagnetic radiation

can be viewed as a stream

of particle-like units called

photons

POSTULATE

hE

3. Properties of Photons

Einitial

Efinal

ABSORPTION OF A PHOTON

E h atoms and molecules

absorb discrete photons

(light quanta)

hp mc

de Broglie

Duality of Wave and Corpuscle

light has properties of a wave and of a particle

SUMMARY

= c E h

hp mc

1. light can be described as a wave of a

wavelength and frequency

2. light can be emitted or absorbed only in discrete quantities (quantum - photon)

3. duality of wave and corpuscle

E n h

hp mc

h

mc

de Broglie wavelength

h

mu

each particle can be described as a

wave with a wavelength λ

4. Properties of Electrons

matter and light (photons) show particle and wave-like properties

WAVE-PARTICLE DUALITY

MASS INCREASES

h h

mu p

WAVELENGTH GETS SHORTER

MASS DECREASES WAVELENGTH GETS LONGER

Wave-likeParticle-like

Baseball Proton PhotonElectron

WAVE-PARTICLE DUALITY

large pieces of matter are mainly particle-like

small pieces of matter are mainly wave-like

MASS

1. light behaves like wave and particle

2. electron behaves like wave and particle

3. electrons are constituents of atoms

4. light is emitted/absorbed from atoms in discrete quantities (quanta)

E h

Einitial

Efinal

EMISSION OF A PHOTON

E h

atoms and molecules

emit discrete photons

electrons in atoms and molecules have discrete

energies

5. Electrons, Photons, Atoms

EMISSION SPECTRAanalyze the wavelengths of the light emitted

only certain wavelengths observed

only certain energies are allowed in the hydrogen atom

Balmer found that these lines have frequencies related

1152

1029.31

41

s

nv

n = 1, 2, 3, 4, 5…

electrons move around the nucleus in only certain allowed circular orbits

e-

THE BOHR ATOM

each orbit has a quantum number associated with it

QUANTUM NUMBERS

n is a QUANTUM NUMBER

n= 1,2,3,4……...

n = 4

n = 3

n = 2

n = 1

n = 4

n = 3

n = 2

n = 1

THE BOHR ATOMQUANTUM NUMBERS and the ENERGY

2

2

n

AZEn

Z = atomic number of atom

A = 2.178 x 10-18 J = Ry

THIS ONLY APPLIES TO ONE ELECTRON ATOMS

OR IONS

BOHR ATOM ENERGY LEVEL DIAGRAM

2

2

n

AZEn

Z=1

2nA

En

HYDROGEN ATOM!

2nA

En En

EN

ER

GY

n=1-A

AA

E 21 1

BOHR ATOM ENERGY LEVEL DIAGRAM

n=1-A

n=2-A/4

En

2nA

En

EN

ER

GY

4222

AAE

BOHR ATOM ENERGY LEVEL DIAGRAM

n=1-A

n=2-A/4

En

n=3-A/9n=4

2nA

En

EN

ER

GY

BOHR ATOM ENERGY LEVEL DIAGRAM

e-Ephoton = h

ELECTRON EXCITATION

n=1-A

n=2-A/4

En

0n=3-A/9n=4

En

erg

y

e-

ELECTRON DE-EXCITATION

emission of energy as a photon

e-

ni

nf

only a photon of the correct energy will do

photonEhE

ABSORPTION OF A PHOTON

2

2

ii

n

AZE

ni

nf

hEEE if ABSORPTION OF A PHOTON

2

2

ff

n

AZE

2

2

2

2

if n

AZ

n

AZE

222 11

fi nnAZE

ni

nf

hEEE if ABSORPTION OF A PHOTON

222 11

fi nnAZE

ni

nf

bsorption)1,2,3...(a if nn

ABSORPTION OF A PHOTON

energy is absorbed

E0

nf

ni

(emission)...3,2,1 fi nn

EMISSION OF A PHOTON

222 11

fi nnAZE

E0This means energy is emitted!

222 11

fi nnAZE

ni

nf

fn

IONIZATION OF AN ATOM

This means energy is absorbed!

E0

E

the ionization energy for one mole is

IONIZATION ENERGY

= 2.178x 10-18 J atom-1 x 6.022x1023 atoms mol-1

=13.12 x 105 J mol-1

= 1312 kJ mol-1

= 2.178 x 10-18 J for one atom

e-

THE BOHR ATOM

QUANTUM NUMBERS

n = 4

n = 3

n = 2

n = 1

222 11

fi nnAZE

E0E0

1;i fn n

absorption

emission

ionization energy

6. HEISENBERG’S UNCERTAINTY PRINCIPLE

x is the uncertainty in the particle’s position

p is the uncertainty in the particle’s momentum

x ph

4

v mp

in the microscopic world you cannot determine the momentum (velocity) and location of a particle

simultaneously

EXP5

THE HEISENBERG UNCERTAINTY PRINCIPLE

Jsh 3410527.0

4

if particle is big then uncertainty small

123410527.0 skgm

x mh

v4

xh

m v

4

1

EXP5

This means we have no idea of the velocity of an electron if we try to tie

it down!

Alternatively if we pin down velocity we have no idea where

the electron is!

So for electrons we cannot know precisely where they are!

we cannot describe the electron as following a known path such as a circular orbit

Bohr’s model is therefore fundamentally incorrect in its description of how the electron behaves.

we cannot know precisely where electrons are!

Schroedinger

(1926)

Born

(1927)

The probability of finding an electron at a given location

is proportional to the square of

2

electron has wave properties

EXP VI

2 – The Bus - Propabilities

orbit of an electron at radius r (Bohr)

probability of finding an electron at a radius r

(Schroedinger, Born)

1. Schroedinger defines energy states an electron can occupy

2. square of wave function defines distribution of electrons around the nucleus

high electron density - high probability of finding an electron at this location

low electron density - low probability of finding an electron at this location

atomic orbital

wave function of an electron in an atom

each wave function corresponds to defined energy of electron

an orbital can be filled up with two electrons (box) EXPVII

most atoms have more than two electrons

each electron in an atom is different

electrons have different ‘labels’ called quantum numbers

QUANTUM NUMBERS

1.principle quantum number

2. angular momentum quantum number

3. magnetic quantum number

4. spin quantum number

1. principle quantum number

nn = 1, 2, 3, 4, 5…

hydrogen atom: n determines the energy of an atomic orbital

measure of the average distance of an electron from nucleus

n increases → energy increases

n increases → average distance increases

e-

n = 4

n = 3

n = 2

n = 1

n = 1 2 3 4 5 6

K L M N O P‘shell’

maximum numbers of electrons in each shell

2 n2

EXP6

2. angular momentum quantum number

l = 0, 1, … (n-1)

l = 0 1 2 3 4 5

s p d f g h

define the ‘shape’ of the orbital

1s, 2s, 3s

3s2s1s

3. magnetic quantum number

ml = -l, (-l + 1), … 0…… (+l-1) +l

defines orientation of an orbital in space

2px, 3px, 4px

4px3px2px

d orbitals

4. spin quantum number

ms = -1/2; + 1/2

ORBITALS AND QUANTUM NUMBERS

1.principle quantum number

2. angular momentum quantum number

3. magnetic quantum number

4. spin quantum number

n = 1, 2, 3, 4, 5…

l = 0, 1, … (n-1)

ml = -l, (-l + 1), … 0…… (+l-1) +l

ms = -1/2; + 1/2

(n, l, ml, ms) ATOMIC ORBITALS

n l ml orbitals designation

1 0 0 1 1s

2 0 0 1 2s

1 -1,0,+1 3 2px,2py,2pz

3 0 0 1 3s

1 -1,0,+1 3 3px,3py,3pz

2 -2,-1,0,+1,+2 5 3dxy,3dyz,3dxz,

3dx2-y2,3dz2

4 … … … …

H Atom Orbital Energies

energy level diagram H atom

3s 3p 3d

2s 2p

1s

E

energy depends only on principal quantum number

orbitals with same n but different l are degenerate

1s

E

2s2p

3s3p

3d4s

4p5s

4d

MULTI-ELECTRON ATOM

orbitals with same n and different l are not degenerate

energy depends on n and ml

EXAMPLES [Xe]

Periodic Table of the Elements

period

group

chemical reactivity - valence electrons

ns1 ns2

ns2np6

ns2(n-1)dx

7. PERIODIC TRENDS

3. IONIZATION ENERGIES

4. ELECTRON AFFINITIES

1. ATOMIC RADIUS

2. IONIC RADIUS

ATOMIC RADIUS

MAIN GROUPS

AT

OM

IC R

AD

IUS

AT

OM

IC R

AD

IUS

1s, 2s, 3s

3s2s1s

2px, 3px, 4px

4px3px2px

ATOMIC RADIUSMAIN GROUPS

ATOMIC RADIUS

effective nuclear charge

IONIC RADII

IONIC RADIUS

ION

IC R

AD

IUS

ION

IC R

AD

IUS

cations are smaller than their atoms

anions are larger than their atoms

Na is 186 pm and Na+ is 95 pm

F is 64 pm and F- is 133 pm

same nuclear charge and repulsion among electrons increases radius

one less electron electrons pulled in by nuclear charge

O < O– < O2–

EXAMPLES

Which is bigger?

Na or Rb Rb higher n, bigger orbitals

K or Ca K poorer screening for Ca

Ca or Ca2+ Ca bigger than cation

Br or Br- Br smaller than anion

QUESTIONThe species F-, Na+,Mg2+ have relative sizes in the order

1 F-< Na+<Mg2+ 2 F-> Na+>Mg2+

3 Na+>Mg2+> F- 4 Na+=Mg2+= F-

5 Mg2+> Na+>F-

QUESTION

1 F-< Na+<Mg2+

2 F-> Na+>Mg2+

3 Na+>Mg2+> F-

4 Na+=Mg2+= F-

5 Mg2+> Na+>F-

Na+ is 95 pm

Mg2+ is 66 pm

F- is 133 pm

ALL 1s22s22p6

ALL are isoelectronic

3. IONIZATION ENERGIES

M(g) M+(g) + e-

energy required to remove an electron from a gas phase atom in its electronic ground state

I1 > 0

first ionization energy(photon)

M+(g) M2+(g) + e-

M2+(g) M3+(g) + e-

second ionization energy

third ionization energy

I2 > 0

I3 > 0

I1 > I2 > I3

Why?

electrons closer to nucleus more tightly held

ION

IZA

TIO

N E

NE

RG

Y

ION

IZA

TIO

N E

NE

RG

Y

first ionization energies decrease

d shell insertion

I E AZ

neff. . 2

2

IONIZATION ENERGY

0

500

1000

1500

2000

2500

0 1 2 3 4 5 6 7 8 9

GROUP NUMBER

ION

IZA

TIO

N E

NE

RG

Y(k

J/m

ol)

1 2 13 14 15 16 17 18

n=1

n=2

n=3

n=4

1. closed shells are energetically most stable

2. half-filled shells are energetically very stable

DERIVATION OF IONIZATION ENERGIES

noble gases have the highest ionization energy

4. ELECTRON AFFINITIES

the energy change associated with the addition

of an electron to a gaseous atom

X(g) + e– X–(g)

electron affinity can be positive or negative

Why?

EL

EC

TR

ON

AF

FIN

ITY

EL

EC

TR

ON

AF

FIN

ITY

general trend

-200

-100

0

100

200

300

400

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

ATOMIC NUMBER

-ELE

CT

RO

N A

FF

INIT

Y

H

He

Li

Be

B

C

N

O

F

Ne

Na

Mg

Al

Si

P

S

Cl

Ar

1. closed shells are energetically most stable

2. half-filled shells are energetically very stable

DERIVATION OF

ELECTRON AFFINITIES