Page 71 - Radiochemistry and nuclear chemistry

60 Radiochemistry and Nuclear Chemistry

explanations of many of the phenomena discussed in this chapter are presented in terms of
simple quantum mechanical rules.

4.2. Conservation laws

In radioactive decay - as well as in other nuclear reactions - a number of conservation
laws must be fulfilled. Such laws place stringent limitations on the events which may occur.
Consider the reaction

X 1 + X 2 --, X 3 + X 4 (4.1)

where X represents any nuclear or elementary particle. In induced nuclear reactions X 1 may
be the bombarding particle (e.g. a 4He atom in a beam of r and X 2 the target
atom (e.g. 14N atoms), and X 3 and X 4 the products formed (e.g. IH and 170).
Sometimes only one product is formed, sometimes more than two. In radioactive decay
several products are formed; reaction (4.1) is then better written X 1 ~ X 2 + X 3. For
generality, however, we discuss the conservation laws for the case (4.1).
For the general reaction (4.1):
(a) The total energy of the system must be constant, i.e.

+ e2 = e3 +e4 (4.2)

where E includes all energy forms: mass energy (w kinetic energy, electrostatic
energy, etc.
(b) The linear momentum

p = mv (4.3)

must be conserved in the system, and thus

Pl + P2 = P3 + P4 (4.4)

The connection between kinetic energy Eki n and linear momentum is given by the relation

Ekin = p2/(2m) (4.5)

(c) The total charge (protons and electrons) of the system must be constant, i.e.

Z 1 +Z 2 =Z 3 +Z 4 (4.6)

where the charge is in electron units.
(d) The mass number (number of nucleons) in the system must be constant, i.e.

A 1 + A 2 = A 3 + A 4 (4.7)