CHEMISTRY 161

Chapter 7

Quantum Theory and Electronic Structure of the Atom

www.chem.hawaii.edu/Bil301/welcome.html

REVISION

= c

E h

1. light can be described as a waves of a

wavelength and frequency

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

3. duality of wave and corpuscle

hp mc

cathode (-)

anode (+)

focus anode (+) fluorescent screen

Deflection of Cathode Rays

particles are negatively charged; particles are defined as ‘electrons’

2. Properties of Electrons

hp mc

h

mc

de Broglie wavelength

h

mu

each particle can be described as a

wave with a wavelength λ

(interferences)

out of phase wave add

destructive interference

in phase wave add

constructive interference

electrometer

gold foil

electron gun

angle (

curr

ent

interference patterns

Diffraction of an electron beam (metal crystal)

WAVE-PARTICLE DUALITY

ph

mh v

matter and energy show particle and wave-like properties

WAVE-PARTICLE DUALITY

MASS INCREASES

h

m v ph

mh v

WAVELENGTH GETS SHORTER

MASS DECREASES WAVELENGTH GETS LONGER

What are the wavelengths of a 0.10 kg ball moving at 35

m/s and an electron moving at 1.0 x 107 m/s?

vmh

)/35)(10.0(10626.6 34

smkgJs

1J = kg m2 s-2

= 1.9 x 10-34 m

Ball:

h = 6.626 x 10-34 J sSolution:

What are the wavelengths of a 0.10 kg ball moving at 35

m/s and an electron moving at 1.0 x 107 m/s?

Solution: h = 6.626 x 10-34 J s

vmh

1J=kg m2 s-2

)/101)(1011.9(10626.6

731

34

smkgJs

= 7.3 x 10-11 m

Electron: kgm 311011.9

What are the wavelengths of a 0.10 kg ball moving at 35

m/s and an electron moving at 1.0 x 107 m/s?

Solution: h = 6.626 x 10-34 J s

vmh

1J=kg m2 s-2

= 1.9 x 10-34 m

= 7.3 x 10-11 mElectron:

Ball:

massive particles have immeasureably small wavelengths

Wave-likeParticle-like

Baseball Proton PhotonElectron

WAVE-PARTICLE DUALITY

large pieces of matter are mainly particle-like, with

very short wavelengths

small pieces of matter are mainly wave-like with longer

wavelengths

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

EMISSION SPECTRAwhite light passing through a prism gives a

continuous spectrum

we can analyze the wavelengths of the light emitted

HYDROGEN DISCHARGE

EMISSION SPECTRAanalyze the wavelengths of the light emitted

only certain wavelengths observed

white light

(continuous spectrum)

experimental evidence

only certain energies are allowed in the hydrogen atom

hydrogen gas

(line spectrum)

CHARACTERISTIC LINE SPECTRUM OF HYDROGEN

Balmer found that these lines have frequencies related

1152

1029.31

41

s

nv

n=3n=4n=5

Niels Bohr

THE BOHR ATOM

THE BOHR ATOM

electrons move around the nucleus in only certain allowed circular orbits

e-

e-

THE BOHR ATOM

as long as an electron remains in a given orbit its energy remains constant and no light is emitted

Bohr’s postulate

electrons move around the nucleus in only certain allowed circular orbits

WHY THE ELECTRON DOES NOT CRASH INTO THE NUCLEUS?

Bohr postulated that the wavelength of the electron just fits the radius of the orbit.

three wavelengths

STABLE

WHY THE ELECTRON DOES NOT CRASH INTO THE NUCLEUS?

five wavelengths

STABLE

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

n=1-A

n=2-A/4

En

0n=3-A/9n=4

En

erg

y

-A/16

e-

n=1-A

n=2-A/4

En

0n=3-A/9n=4

En

erg

y

-A/16

e-

ELECTRON EXCITATION

2nA

En

excite electron to a higher energy level

n=1-A

n=2-A/4

En

0n=3-A/9n=4

En

erg

y

e-

to excite the electron we need energy

this can be in the form of a photon

Ephoton = h

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

This means 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!

hydrogen emission spectrum

n = 1 Ground state

n = 2

n = 3n = 4n = Ion8

Excited states

...

En

erg

yFor the Lyman series, nf= 1 and ni = 2,3,4…

For the Balmer series, nf = 2 and ni = 3,4,5…

For the Paschen series, nf = 3 and ni = 4,5,6…

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

WAVELENGTH OF PHOTON

IE = 2.178 x 10-18 J for one H atomH H+ + e–

E hc

e-

QUANTUM NUMBERS

n = 4

n = 3

n = 2

n = 1

SUMMARY

THE BOHR ATOM

222 11

fi nnAZE

Z = atomic number of atom

A = 2.178 x 10-18 J = Ry

Homework

Chapter 7, pages 252-263 problems