PHY3063 Spring 2006
R. D. Field
Exam 2
Page 1 of 8
March 9, 2006
PHY 3063 Exam 2 Name_____________________
Problem 1 (25 points):
Consider an “atom” consisting of a proton and a muon.
A proton has an
electric charge +e and rest mass energy M
p
c
2
≈
940 MeV.
A muon is an elementary particle with
charge –e similar to an electron but with a mass that is 207 times the mass of an electron (m
e
c
2
≈
0.511 MeV). Use Bohr’s model of an atom to calculate the following:
(a) (8 points)
The radius of the first Bohr orbit (
i.e.
the ground state) of the muonic “atom” (
in
fm
).
(b) (8 points)
The ground state energy of the muonic “atom” (
in keV
).
(c) (9 points)
The ground state energy of the hydrogen atom can be estimated using the
uncertainty relation.
For a hydrogen atom in the ground state the uncertainty
∆
r
in the position
of the electron is approximately the 1
st
Bohr radius,
r
0
, consequently the electron’s momentum
p
r
is uncertain by about
r
∆
/
h
.
Compute the ground state energy of the hydrogen atom (
in eV
),
r
Ke
m
p
E
e
r
2
2
2
−
=
,
by setting
r = r
0
and
0
/
r
p
p
r
r
h
=
∆
=
, where
r
0
is the Bohr radius of the ground state.
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PHY3063 Spring 2006
R. D. Field
Exam 2
Page 2 of 8
March 9, 2006
PHY 3063 Exam 2 Name_________________
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 Spring '07
 Field
 Physics, Charge, Energy, Mass, Sin, Cos, R. D., R. D. Field

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