p45_003.pdf
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Chapter 45 - 45.3
3. Conservation of momentum requires that the gamma ray particles move in opposite directions with
momenta of the same magnitude. Since the magnitude
p
of the momentum of a gamma ray particle is
related to its energy by
p
=
E/c
, the particles have the same energy
E
. Conservation of energy yields
m
π
c
2
=2
E
,where
m
π
is the mass of a neutral pion. According to Table 45-4, the rest energy of a neutral
pion is
m
π
c
2
= 135
.
0 MeV. Hence,
E
= (135
.
0MeV)
/
2=67
.
5 MeV. We use the result of Exercise 3 of
Chapter 39 to obtain the wavelength of the gamma rays:
λ
=
1240 eV
10
6
eV
=1
.
84
·
nm
×
10
−
5
nm = 18
.
4fm
.
67
.
5
×
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