p43_061 - energy K e is related to its momentum by the...

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61. Since the electron has the maximum possible kinetic energy, no neutrino is emitted. Since momentum is conserved, the momentum of the electron and the momentum of the residual sulfur nucleus are equal in magnitude and opposite in direction. If p e is the momentum of the electron and p S is the momentum of the sulfur nucleus, then p S = p e . The kinetic energy K S of the sulfur nucleus is K S = p 2 S / 2 M S = p 2 e / 2 M S ,wh e r e
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Unformatted text preview: energy K e is related to its momentum by the relativistic equation ( p e c ) 2 = K 2 e + 2 K e mc 2 , where m is the mass of an electron. See Eq. 38-51. Thus, K S = ( p e c ) 2 2 M S c 2 = K 2 e + 2 K e mc 2 2 M S c 2 = (1 . 71 MeV) 2 + 2(1 . 71 MeV)(0 . 511 MeV) 2(32 u)(931 . 5 MeV / u) = 7 . 83 10 5 MeV = 78 . 3 eV where mc 2 = 0 . 511 MeV is used (see Table 38-3)....
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