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CHEMISTRY 161
Chapter 7
Quantum Theory and Electronic Structure of the Atom
www.chem.hawaii.edu/Bil301/welcome.html
REVISION
1. light can be described as a wave (wavelength) and a particle (momentum)
2. electrons can be described as a particle (momentum) and a wave (wavelength)
E  h
 = u
p
h

 mu
3. light is emitted/absorbed from atoms/molecules in discrete quanta
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
HEISENBERG’S
UNCERTAINTY PRINCIPLE
in the microscopic world you cannot determine the
momentum 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
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
(1926)
H = E 
2

Born
The probability of finding an
(1927)
electron at a given location
is proportional to the square
of .
PARTICLE IN A BOX
orbit of an electron at radius r
(Bohr)
H = E 
probability of finding an electron at
a radius r
(Schroedinger, Born)
1. Schroedinger equation defines energy states an electron can occupy
H = E 
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
2

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
2
2
n
n=2
n=1
e-
radial distribution maximum of
electron density corresponds
to Bohr radii
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
sperical
polar
cloverleaf
3. magnetic quantum number
ml = -l, (-l + 1), … 0…… (+l-1) +l
defines orientation of an orbital in space
4. spin quantum number
ms = -1/2; + 1/2
SUMMARY
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
Homework
Chapter 7, pages 263-267
problems