Since, however, the intermediate product E has a much more rapid rate of change than D or F, the equations can be simplified, without much loss of accuracy, by disregarding the change E, and by supposing that D gives out β rays and changes directly into the α ray product F.
Let λ1, λ2 be the constants of change D and F respectively. Let n₀ be the number of particles of D present initially. Then using the notation of [section 197], the amount P of radium D at any time t is given by
The amount Q of radium F is given by
Fig. 96.
The number of β particles emitted by D + E per second, some months afterwards, is
and the number of α particles emitted by radium F is