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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
=−=




= 

