Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

90 CHAPTER 4
This transformation shows that beta decay occurs among those nuclides that have a
surplus of neutrons. For beta emission to be energetically possible, the exact nuclear
mass of the parent must be greater than the sum of the exact masses of the daughter
nucleus plus the beta particle.
Mp = Md + Me + Q. (4.7)
This restriction, of course, is analogous to the corresponding restriction on alpha
emitters. Because a unit negative charge is lost during beta decay and the mass of the
beta particle is ≪1 amu, the daughter nucleus is one atomic number higher than
its parent but retains the same atomic mass number as the parent. For example,
radioactive phosphorus decays to stable sulfur according to the equation
32
15
P → 32
16
0
S + −1e + 1.71 MeV.
The transformation energy, in this instance 1.71 MeV, is the energy equivalent of
the difference in mass between the 32 P nucleus and the sum of the masses of the
32 S nucleus and the beta particle, and appears as kinetic energy of the beta particle.
If neutral atomic masses are used to complete the mass–energy equation, then, of
course, the mass of the electron shown in the right-hand side of Eq. (4.7) is not
considered since it is implicitly included in the extranuclear electronic structure of
the 32 S. The mass difference is
31.973907 = 31.972070 + Q
Q = 0.001837 amu
and the energy equivalent of the mass difference is
0.001837 × 931 MeV/amu = 1.71 MeV.
Examination of Eq. (4.5) shows that in the case of beta emission, an extremely
small part of the energy of the reaction is dissipated by the recoil nucleus since m/M
(where m is now the mass of the beta particle and M is the mass of the daughter
nucleus) is very small. In the example given above,
m 0.00055
= = 0.000017
M 32
and Q is only 1.000017 times greater than the kinetic energy of the beta particle.
On the basis of the above analysis, one might expect beta particles to be monoenergetic,
as in the case of alpha radiation. This expectation is not confirmed
by experiment. Instead, beta particles are found to be emitted with a continuous
energy distribution ranging from zero to the theoretically expected value based on
mass–energy considerations for the particular beta transition. In the case of 32 P, for
example, although the maximum energy of the beta particle may be 1.71 MeV, most
of the betas have considerably smaller kinetic energies, as shown in Figure 4-4. The
average energy of a 32 P beta particle is 0.7 MeV or about 41% of the maximum energy.
Generally, the average energy of the beta radiation from the most beta-active