CHEMISTRY 161
Chapter 7
1. Structure of an Atom
subatomic particles
electrons
protons
neutrons
mass number
17e
17p
35
17
18n
Cl
18 neutrons
atomic number
Why are atoms stable?
e-
classical physics
predicts that electron
falls into nucleus
2. Waves
.
wavelength [m]
l
.
amplitude
Intensity
direction of
propagation
distance, x
EXP1
v = x/t
t = x/v
T
.
direction of
Intensity
.
period [s]
propagation
time, t
Frequency [s-1]
1

T
[1 Hz = 1 s-1]
Hertz
Frequency and Wavelength
l = c
wavelength
meter (m)
frequency
Hz or s-1
speed of radiation
m s-1
LONG WAVELENGTH, LOW FREQUENCY
light can be described as a wave
POSTULATE
visible light consist of
electromagnetic waves
speed of propagation
(speed of light)
James Maxwell
c = 3  108 ms-1
light has two components
1.electric field
2.magnetic field
ELECTROMAGNETIC SPECTRUM

l
INCREASING FREQUENCY & ENERGY
EXP2
VISIBLE SPECTRUM
Wavelength l (nanometers)
l = c
Which color has the higher frequency?
1 = orange
2 = blue
The wavelength of the yellow light from a lamp is 589 nm.
What is the frequency of the radiation?
c  l
l  589nm  5.89 10 m
7
1
2.998  10 ms
14 1
 
 5.09  10 s
7
l
5.89  10 m
c
8
3. Postulates
Li
Na
K
different atoms emit distinct light
EXP3
E  h
h is Planck’s constant
h = 6.626 x 10-34 J s
Max Planck
energy can be emitted or absorbed only
in discrete quantities (little packages)
EXP4/5
Emission Nebula
CLASSICAL
any amount of energy can be emitted or absorbed
E  h
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
3. Properties of Photons
POSTULATE
Electromagnetic radiation
can be viewed as a stream
of particle-like units called
photons
Albert Einstein
E  h
ABSORPTION OF A PHOTON
Efinal
atoms and molecules
E  h 
absorb discrete photons
(light quanta)
Einitial
EXP6
Duality of Wave and Corpuscle
light has properties of a
wave and of a particle
p
de Broglie
h
l
 mc
SUMMARY
1. light can be described as a wave of a
wavelength and frequency
E  h
l = c
2. light can be emitted or absorbed only in discrete quantities
(quantum - photon)
E  n h 
3. duality of wave and corpuscle
p
h
l
 mc
4. Properties of Electrons
de Broglie wavelength
p
h
l
 mc
h
l
mc
h
l
mu
each particle can be described as a
wave with a wavelength λ
WAVE-PARTICLE DUALITY
matter and light (photons) show particle and wave-like properties
h
h
l

mu p
MASS INCREASES
WAVELENGTH GETS SHORTER
MASS DECREASES
WAVELENGTH GETS LONGER
WAVE-PARTICLE DUALITY
large pieces of matter are mainly particle-like
small pieces of matter are mainly wave-like
MASS
Baseball Proton
Particle-like
Electron
Photon
Wave-like
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 
5. Electrons, Photons, Atoms
EMISSION OF A PHOTON
atoms and molecules
Einitial
emit discrete photons
E  h 
Efinal
electrons in atoms and
molecules have discrete
energies
EMISSION SPECTRA
analyze 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
1 1

15 1
v    2   3.29  10 s
4 n 
n = 1, 2, 3, 4, 5…
THE BOHR ATOM
electrons move around the nucleus in only
certain allowed circular orbits
QUANTUM NUMBERS
n=4
n=3
n=2
n=1
e-
each orbit has a quantum
number associated with it
n is a QUANTUM NUMBER
n= 1,2,3,4……...
THE BOHR ATOM
QUANTUM NUMBERS and the ENERGY
n=4
n=3
n=2
n=1
En  
AZ
n
2
2
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
En  
Z=1
AZ
n
2
2
HYDROGEN ATOM!
A
En   2
n
BOHR ATOM ENERGY LEVEL DIAGRAM
ENERGY
En
-A
A
En   2
n
A
E1   2   A
1
n=1
BOHR ATOM ENERGY LEVEL DIAGRAM
En
ENERGY
-A/4
-A
A
En   2
n
A
A
E2   2  
2
4
n=2
n=1
BOHR ATOM ENERGY LEVEL DIAGRAM
En
-A/4
n=2
ENERGY
-A/9
n=4
n=3
-A
e-
n=1
A
En   2
n
Ephoton = h
ELECTRON EXCITATION
ELECTRON DE-EXCITATION
En
n=4
n=3
0
-A/9
e-
Energy
-A/4
-A
n=2
emission of energy as a photon
e-
n=1
ABSORPTION OF A PHOTON
nf
only a photon of the correct
energy will do
ni
E  h  E
photon
ABSORPTION OF A PHOTON
E  E f  Ei  h
nf
AZ
Ei   2
ni
2
AZ
Ef   2
nf
ni
2
ABSORPTION OF A PHOTON
E  E f  Ei  h
nf
ni
 AZ 2   AZ 2 
E    2     2 
 n   n 
f 
i



1
1
2

E  AZ

 n2 n2 
f 
 i
ABSORPTION OF A PHOTON
nf


1
1
2

E  AZ

 n2 n2 
f 
 i
n f  ni  1,2,3...(absorption)
E0
ni
energy is absorbed
EMISSION OF A PHOTON
ni


1 
2 1
E  AZ

 n2 n2 
f 
 i
ni  n f  1,2,3...(emission)
E0
nf
This means energy is emitted!
IONIZATION OF AN ATOM
nf
ni


1
1
2

E  AZ

 n2 n2 
f 
 i
nf  
E0
This means energy is absorbed!
IONIZATION ENERGY
E = 2.178 x 10-18 J for one atom
the ionization energy for one mole is
= 2.178x 10-18 J atom-1 x 6.022x1023 atoms mol-1
=13.12 x 105 J mol-1
= 1312 kJ mol-1
THE BOHR ATOM


1
1

QUANTUM NUMBERS E  AZ 2 

 n2 n2 
f 
 i
n=4
n=3
n=2
n=1
e-
E0
E0
absorption
emission
ni  1; n f  
ionization energy
6. HEISENBERG’S
UNCERTAINTY PRINCIPLE
in the microscopic world you cannot determine the
momentum (velocity) and location of a particle
simultaneously
x is the uncertainty in the particle’s position
p is the uncertainty in the particle’s momentum
h
xp 
4
p  m v
EXPVII
THE HEISENBERG UNCERTAINTY PRINCIPLE
h
x  mv 
4
h
 34
2 1
 34
 0.527  10 Js  0.527  10 kgm s
4
h 1
x  v 

4 m
if particle is big then
uncertainty small
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 know precisely where electrons 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.
Schroedinger
Born
(1926)
(1927)
electron has wave properties

2

The probability of finding an
electron at a given location
is proportional to the square
of 
2 – The Bus - Probabilities
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) EXPVIII
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
n
n = 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
n=1 2 3 4 5 6
‘shell’
K L M N O P
maximum numbers of electrons in each shell
n=4
n=3
n=2
n=1
e-
2
2
n
EXP8
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
EXPIX
1s, 2s, 3s
1s
2s
3s
3. magnetic quantum number
ml = -l, (-l + 1), … 0…… (+l-1) +l
defines orientation of an orbital in space
2px, 3px, 4px
2px
3px
4px
d orbitals
4. spin quantum number
ms = -1/2; + 1/2
ORBITALS AND QUANTUM NUMBERS
1.principle quantum number
n = 1, 2, 3, 4, 5…
2. angular momentum quantum number
l = 0, 1, … (n-1)
3. magnetic quantum number
ml = -l, (-l + 1), … 0…… (+l-1) +l
4. spin quantum number
ms = -1/2; + 1/2
ATOMIC ORBITALS
(n, l, ml, ms)
n
1
l
0
ml
0
orbitals
1
designation
1s
2
0
0
1
2s
1
-1,0,+1
3
2px,2py,2pz
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
…
3
4