This preview shows page 1. Sign up to view the full content.
PHY4604
R. D. Field
Department of Physics
Chapter5_7.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
centerofmass
is at the point
x
determined by
m
e
(rx) = Mx
and hence
M
m
r
m
x
e
e
+
=
and
M
m
Mr
x
r
e
+
=
−
The
total angular momentum
is
ω
µ
2
2
2
2
)
(
r
r
M
m
M
m
Mx
x
r
m
L
e
e
e
=
+
=
+
−
=
,
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.
 Spring '07
 FIELDS
 mechanics, Charge, Force

Click to edit the document details