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1
 
 
 
2
A muonic atom consists of a muon
mass 106 / and charge -
in place of an electron. For the muon in a
hydrogen atom, what is a the smallest
radius and b the binding energy of the
muon in the gr
m MeV c q e
 
ound state?
Solution

3
2
2
Let be the reduced mass,
106
be the mass
of muon, 938.27
be the mass of the proton,
then
MeV
m
c
MeV
M
c




4
2 2
2 2
2
2
2
2
=
106 938.27
106 938.27
99456.62( )
1044.27
95.24
mM
m M
MeV MeV
X
c c
MeV MeV
c c
MeV
c
MeV
c
MeV
c







5
(a)
2
0
0 2
2
12
2
15 2
2
19 2
2 2 2
42
2
38 6 2
2
Using
8.854 10
.
(4.136 10 . )
3.14 95.24
(1.602 10 )
. .
151.46 10
.
767.49 10 10
h
a
e
C
X X
N m
X eV s
MeV
X X
c
X C
C eV s
X
N m
eV
X X XC
c











6
10 2 2
2
10
2
16 2
2
2
6
6 19
13
13
13
0.197 10 . .
.
0.197 10 9
10 . .
.
1.78 10
1.78 10 1.602 10
2.85 10
2.85 10 .
2.85 10
X eV s c
N m
X X X
m
eV s
s
N m
X eV
N
X X X J
N
X J
N
X N m
N
X m














7
(b)
4
2 2
0
2
2
15 2
Using
2 (4 )
95.24
(1.440 . )
2 (4.136 10 . )
1
4 3.14 3.14
me
E
MeV
X
c
eV nm
X X eV s X
X X





8
6
2
2 18 2
30 2 2
2
12
2
30 2
18 2
2 2
18 2
2
16 2
2
2
95.24 10
2.07 10
0.87 10 .
.
197.15 10
0.87 10
226.61 10 .
.
226.61 10 .
9 10 .
25.18 10
2518
eV
X X
c
XeV X m
X eV s
eV m
X
c
X s
X eV m
c s
X eV m
m
X s
s
X eV
eV











�ݺ�ߣ

Stephen 4.31.doc

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Stephen 4.31.doc