Page 73 - Radiochemistry and nuclear chemistry

62 Radiochemistry and Nuclear Chemistry

disappearance of mass, cf. eqns. (3.2) and (3.5). This energy is also called the Q-value of
the reaction

Q (MeV) = -931.5AM (u) (4.12)

For a-decay we can define the Q-value as

Qo~ = -931"5(Mz-2 + MHe - MZ) (4.13)

We always write the products minus the reactants within the parenthesis. A decrease in total
mass in a-decay means a release of energy. The minus sign before the constant 931.5 is
necessary to make Q positive for spontaneous decay.
An example will show the use of this equation. For the decay reaction 238U --) 234Th +
4He, the mass values for 238U and 4He are in Table 3.1; for 234Th it is 234.043 594. Thus
we obtain Qa = -931.5 (234.043 594 + 4.002 603 - 238.050 7785) = 4.274 MeV.
If the products are formed in their ground states, which is common for a-decay, the total
decay energy is partitioned into the kinetic energies of the daughter nucleus (E z_ 2) and the
helium nucleus (Ea):

Qot = EZ- 2 + Eo~ (4.14)

Because of conservation of energy (4.2) and momentum (4.4)

EZ_ 2 = Qa Ma /M z (4.15)

and

Et~ = Qa MZ_ 2/M Z (4.16)

From these equations we can calculate the kinetic energy of the 234Th daughter to be 0.072
MeV, while that of the a-particle is 4.202 MeV. Because of the large mass difference
between the a-emitting nucleus and the helium atom, almost all of the energy is carried
away with the a-particle.
Although the kinetic energy of the daughter nucleus is small in comparison with that of
the a-particle, it is large (72 000 eV) in comparison with chemical binding energies (< 5
eV). Thus the recoiling daughter easily breaks all chemical bonds by which it is bound to
other atoms.
In 1904 it was observed by H. Brooks that measurements on 218po (RaA), obtained from
radon, led to a contamination of the detection chamber by 214pb (RaB) and 214Bi (RaC).
This was explained by Rutherford as being due to daughter recoil m the a-decay of 218po
in the sequence (written symbolically):

222Rn(c~, 3.8 d) 218po(a, 3.05 min) 214pb(~-, 27 min) 214Bi(~J-, 20 rain)...