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 pe is the momentum of the electron and pS is the
momentum of the sulfur nucleus, then pS = -pe. The kinetic energy KS of the sulfur nucleus is
KS = p2 /2MS = p2/2MS, where MS is the mass of the sulfur nucleus. Now, the electron s kinetic
S e
2
energy Ke is related to its momentum by the relativistic equation (pec)2 = Ke +2Kemc2, where m is
the mass of an electron. See Eq. 38-51. Thus,
2
(pec)2 Ke +2Kemc2 (1.71 MeV)2 +2 (1.71 MeV)(0.511 MeV)
KS = = =
2MSc2 2MSc2 2(32 u)(931.5MeV/u)
= 7.83 × 10-5 MeV = 78.3 eV
where mc2 =0.511 MeV is used (see Table 38-3).