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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