PHY3063
R. D. Field
Department of Physics
Chapter4_4.doc
University of Florida
Bohr’s Model of the One Electron Atom
Assume that the nucleus with charge
+Ze
is at rest and the
electron travels in a circular orbit around the proton (
i.e.
assume
M
nucleus
>> m
e
).
The force on the electron is
r
v
m
a
m
r
KZe
F
e
e
2
2
2
=
=
=
and
2
2
2
r
KZe
r
v
m
e
=
.
Hence, we must replace
e
2
by
Ze
2
in all the formulas.
Thus,
0
2
r
Z
n
r
n
=
,
c
Z
n
v
n
α
1
=
,
and
0
2
2
E
n
Z
E
n
=
.
Correction for a Finite Nuclear Mass:
Let the nucleus have mass
M
and speed
V
and the
electron mass
m
e
and speed
v
e
.
Then the
center-of-mass
is at the point
x
determined by
m
e
(r-x) = Mx
and hence
M
m
r
m
x
e
e
+
=
and
M
m
Mr
x
r
e
+
=
−
The
total angular momentum
is
ω
µ
ω
ω
ω
2
2
2
2
)
(
r
r
M
m
M
m
Mx
x
r
m
L
e
e
e
=
+
=
+
−

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