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Quantum Theory
3
Section 4-3
1
Topics

The Bohr Model

Summary
2
The Bohr Model
While working
in Rutherford’s
lab, Niels Bohr
proposed that
electrons move
in circular orbits
about the nucleus
3
The Bohr Model
Unfortunately, classical
physics predicts that such
orbits are not stable because
the electrons would radiate
away their energy and
spiral into the
nucleus in about
10-8 seconds
4
The Bohr Model
Bohr postulated:
1. electrons can move only
in certain orbits without
radiating
Ei
Ef
2. atoms radiate when the
electron transitions from
one orbit to another and
the frequency f of the radiation is given by
hf  Ei  Ef
5
The Bohr Model
In Bohr’s 1913 paper, he
showed that his frequency
condition implied that
angular momentum is quantized
in units of h / 2p
h
L  mvr  n
n
2p
n  1, 2,3, ....
Ei
Ef
6
The Bohr Model
Newton’s law for circular
motion
e
F  ma  mv / r
2
Electric force
Q = Ze
eQ
F k 2
r
Quantization condition
mvr  n
from these formulae…
7
The Bohr Model
…it follows that
a0
rn  n
Z
e
2
where
a0 
Q = Ze
2
mke
2
 0.0529nm
is the Bohr radius and
Q  Ze
is the electric charge of the
nucleus
8
The Bohr Model
Assuming the electron speed
is small compared with that
of light, the total energy
of the electron is
1 2  kZe 
E  mv   

2
r 

kZe 2

2r
2
e
Q = Ze
Finally, when we substitute the formula
for r we get…
9
The Bohr Model
…the total energy of the
nth orbit
e
2
Z
En  E0 2
n
Q = Ze
where
2 4
mk e
E0 
 13.6 eV
2
2
10
The Bohr Model
Therefore Bohr’s
frequency postulate
Ei  E f
f
h
e
Q = Ze
becomes
E0 Z
f  c/ 
h
2
 1 1
 2  2 
 n f ni 
12
Energy levels of hydrogen
13.6
En   2 eV
n
13
Summary

The Bohr Model
 This was the first successful model of
simple atoms like hydrogen

But, unfortunately, its extension to
complex atoms was not very successful
14
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