Question 15.6: The 77 32Ge isotope decays by two successive β-decay process...
The ^{77}_{ 32}Ge isotope decays by two successive β-decay processes to ^{77}_{ 34}Se. Calculate the Q-values for each of these decay processes. What are the maximum kinetic energies of the emitted electrons?
The formulas for the two decay processes are
^{77}_{ 32}Ge →^{77}_{ 33} As + e^{−} + ν^{-}_{e} ,and
^{77}_{ 33}As →^{77}_{ 34} Se + e^{−}+ ν^{-}_{e} .
^{77}_{34}Se is the only stable isotope with A = 77.
The Q-value for each of these decay processes can be calculated using Eq. (15.15). For the first decay process, the Q-value is
Q = [m(^{A} _{Z}X) − m(^{A}_{ Z+1}X^\prime )]c^{2} , (15.15)
Q = [76.923549 u − 76.920648 ] 931.5 MeV/u = 2.70 MeV ,
while for the second decay process the Q-value is
Q = [76.920648 u − 76.919915 ] 931.5 MeV/u = 0.68 MeV .
The maximum values of the kinetic energy of the electrons emitted in these two decays is slightly less than the Q-values due to the small amount of kinetic energy carried off by the daughter nuclei.