Class Notes (1,200,000)
CA (650,000)
McGill (40,000)
Chemistry (1,000)
CHEM 110 (300)
Lecture

The Bohr Atom


Department
Chemistry
Course Code
CHEM 110
Professor
Bryan Sanctuary

Page:
of 3
Bohr atom:
The Model: see diagram. Assume classical motion with the centripetal force given by the Coulomb
attraction. Assume angular momentum is quantized. Put these into
mathematical form.
1: Balance for forces, solve for velocity
Centripetal
22
2
2
2
2
4
4
C
e
o
o
FF
mu Ze
rr
Ze
ur
πε
πε
=
=
=r
22
2
44
e
oe oe
m
Ze Ze
uu
mr mr
πε πε
= →=
2: Kinetic energy of electron
2
11
22
ee
KE m u m= =
2
4
oe
Ze
m
πε
2
8
o
Ze
r
r
πε
=
3. Potential energy is Coulomb energy:
22
2
44
oo
Ze Ze
PE F r r
rr
πε πε
= ×= ×=
4. Total energy
22 2
84 8
oo o
Ze Ze Ze
E KE PE rr r
πε πε πε
=+= − =
5. Angular momentum (quantization assumption)
Classical Quantum
Angular Momentum assumption
2 22
2
2
1,2.....
2
44
4
e
e
ee
oe oe
e
o
h
L m ur n n n
Ze m r
Ze
L n m ur m r
mr mr
Ze m r
Ln
π
πε πε
πε
= ×
= =≡=
= = = =
= =
Lrp
6. Solve for the radii where the electron can be
2
2
22
22
2
4
4
4 1,2,...
en
o
en
o
o
n
e
Ze m r
Ln
Ze m r
n
r nn
Ze m
πε
πε
πε
= =
=
= = ∞
7. Quantized energy
( )
( )
22
22
2
24
22
2
84
8
1
24
n
on o
oe
e
n
o
Ze Ze
Ern
Ze m
Zem
En
πε πε
πε
πε
=−=




= 


8. Bohr radius: Z=1, n=1.
To test the model, compare with experiment: Emission spectroscopy, Ionization energy, Energy levels,
Bohr radius. Since they all agree, visualize the motion of the electron as Bohr did. This picture in your
mind is based upon the mathematical equations. There is no other way.
Bohr guessed a model and tested it. It is always a similar procedure.
B. Sanctuary
McGill University