203. Effect of a rayless change on the activity curves. Certain important cases occur in the analysis of radio-active changes, when one of the products does not give rise to rays and so cannot be detected directly. The presence of this rayless change can, however, be readily observed by the variations which occur in the activity of the succeeding product.
Let us consider, for example, the case where the inactive matter A, initially all of one kind, changes into the matter B which gives out rays. The inactive matter A is supposed to be transformed according to the same law as the radio-active products. Let λ1, λ2 be the constants of the change of A and B respectively. If n is the number of particles of A, initially present, we see from the equation (4), section 197, that the number of particles of the matter B present at any time is given by
Differentiating and equating to zero, it is seen that the value of Q passes through a maximum at a time T given by the equation
