Page 80 - Radiochemistry and nuclear chemistry

Unstable Nuclei and Radioactive Decay 69

Note that like the case of the negatron decay, it is not necessary to add or subtract electron
masses in the calculation of the Q-value in EC. An example of EC is the decay of 7Be to
7Li for which it is possible to calculate that the Q-value is 0.861 MeV. This reaction is
somewhat exceptional since for neutron deficient nuclei with values of Z below 30, positron
emission is the normal mode of decay. Electron capture is the predominant mode of decay
for neutron deficient nuclei whose atomic number is greater than 80. The two processes
compete to differing degrees for the nuclei between atomic numbers 30 and 80. Electron
capture is observed through the emission of electrons from secondary reactions occurring
in the electron shell because of the elemental change (see w

4.4.8. Daughter recoil

If the B-particle and the neutrino are emitted with the same momentum but in opposite
direction, the daughter nucleus experiences no recoil. On the other hand, if they are both
emitted in the same direction, or if all the energy is carried away with one of the particles,
the daughter experiences maximum recoil. The daughter therefore recoils with kinetic
energies from zero up to a maximum value (when the/~-particle is emitted with maximum
energy). We can therefore write

QB = Ed + Emax (4.31)

where E d is the recoil energy of the daughter nucleus. From the laws of conservation of
energy and momentum, and taking the relativistic mass changes of the electron into
account, one finds that the daughter recoil energy is

Ea = me Emax/m d + Emax2/(2 md g2) (4.32)

The recoil energy is usually - 100 eV, which still is sufficient for causing atomic
rearrangements in surrounding molecules. In the decay of 14C (to N), Ema x is 0.155 MeV,
which gives E d = 7 eV. However, by labeling ethane, 14CH314CH3 , with 14C in both C
14
positions, it was found that CH3NH 2 was formed in 50% of the cases when one of the
14C atoms in ethane had decayed, although the C =--N bond strength is only 2.1 eV; most
of the decays occur with less than the maximum recoil energy, which also can be averaged
over the whole molecule. The small recoil also explains why decay reactions like

127TEO32- -~ 127IO 3- + ~-

and

52MNO4- ~ 52CRO42- + /3 +

are possible, even when E d is tens of electron volts. However, secondary effects tend to
cause the chemical bond to break following radioactive decay (see w