The radioactive decay of unstable nuclei is a com­pletely random process and it is not possible to pre­dict when a particular nucleus is going to decay. When there are a large number of radioactive nuclei, however, one can statistically state that the proba­bility of decay per unit time is constant. That is, the number of nuclei likely to decay in an infinitesimal time interval is proportional to the number (N) pre­sent. Thus dN/dt = XN where X is the constant of proportionality and is known as the decay constant; its value depends on the particular radioactive isotope and is unique to that isotope. dN/dt is negative be­cause N is decreasing. Integration gives N = No exp (-Xt), the familiar exponential function where No is the number of radioactive nuclei of a particular isotope at time t = 0.

The rate at which nuclei decay is often given in terms of the mean lifetime of a nucleus, r, or alter­natively in terms of the half value period, T±, often abbreviated to the half life, r is the inverse’ of the decay constant X and it follows from the exponential form of the decay that:

 

The a particle is identical to the helium nucleus 4He and the above may also be written:

 

4-

 

He

 

Thorium

 

a particle

 

Alpha emission tend to be from the heavier elements (Fig 1.4). • Spontaneous fission A further type of radioacti­vity is ‘spontaneous’ fission in which the nucleus splits into two roughly equal portions. Spontane­ous fission is confined to the heavy elements and in general is barely detectable in competition with the more prevalent a decay. Examples of dements which undergo spontaneous fissions are U-238 with about 26 fissions/gm h and Pu-240 with 106 fis — sions/gm h. Spontaneous fission is not to be con­fused with neutron induced fission, the basis of nuclear reactors, and which will be discussed later.