Page 77 - Radiochemistry and nuclear chemistry

66 Radiochemistry and Nuclear Chemistry

The last term is approximately the kinetic energy of the particle (2.5) divided by c 2, and
thus

m ~ m ~ + Eki n/c 2 (4.21)

The increase in mass, Am = m - m ~ because of the kinetic energy of the particle,

Eki n = Amc 2 (4.22)

was generalized by A. Einstein in the special theory of relativity, leading (after more
detailed calculations) to the well known mass-energy relationship

E = mc 2 (4.23)

which we already have applied in the discussion of the nuclear binding energy (3.3).
When a neutrino is ejected from the nucleus it carries away energy of kinetic nature.
Thus, according to (4.21) the neutrino has a relativistic mass > 0, and obviously also a
momentum p = mv. Recoil studies of/3-decay have proven this to be true.
In order to correctly apply (4.18) for the calculation of the/3-decay energy, the relativistic
electron mass must be used; as is seen from Figure 4.2, already at 0.1 MeV, the relativistic
mass of the electron is 15 % larger than the rest mass m o (In the following the rest masses
e"
of the electron, neutron, etc., will be denoted simply as m e, m n, etc.; capital M if in
universal mass units, u)
The energy released in/3-decay is distributed between the neutrino, the electron, and the
recoil of the daughter nucleus. This latter will be much smaller than the first two and can
be neglected in a first approximation (w Therefore, the total B-decay energy can be
considered to be distributed between the neutrino and the electron. For the decay 137Cs
137tuBa it can be shown that the total decay energy QB is 0.514 MeV. This is also termed
Ema x. The neutrino energy spectrum is the complement of the/3-particle energy spectrum.
If the energy of the electron is 0.400 MeV, that of the neutrino is 0.114 MeV. If the
electron energy is 0.114 MeV, the neutrino energy is 0.400 MeV.
In/3--decay the average value of the/3--particle energy is approximately 0.3 Ema x. In
positron emission, the average energy of the/3+-particle is approximately 0.4 Ema x.
The assumption that the neutrino has a zero rest mass has been questioned by
experimentalists and theorists. A number of experiments have established an upper limit of
the rest mass as < 10 eV. The implications of a finite rest mass are broad as the nature of
the neutrino and the theory of beta decay is involved. On an even grander scale, the
expansion of the universe depends on the neutrino mass. If the neutrino rest mass is only
a few eV, this might result in sufficiently greater gravitational force that could eventually
stop the expansion and contraction will begin, see Ch. 17.