deposit on removal consists in general of a mixture of the products radium A, B, and C. The nature of the rays from each product, the time for each product to be transformed, and the value of λ are tabulated below for convenience:—
Product Rays T. λ (sec^{-1})
Radium A α rays 3 min. 3·85 × 10^{-3}
Radium B no rays 21 min. 5·38 × 10^{-4}
Radium C α, β, γ rays 28 min. 4·13 × 10^{-4}
Since only the product C gives rise to β and γ rays, the activity measured by either of these types of rays will be proportional to the amount of C present at any time, i.e. to the value of R at any time. For a long exposure, the variation of activity with time measured by the β and γ rays will thus be represented by the upper curve CC of Fig. 73, where the ordinates represent activity. This curve will be seen to be very similar in shape to the experimental curve for a long exposure which is given in Fig. 68.
Since radium B does not give out rays, the number of α particles expelled from the active deposit per second is proportional to λ_{1}P + λ_{3}R. The activity measured by the α rays, using the electrical method, is thus proportional at any time to λ_{1}P + Kλ_{3}R, where K is a constant which represents the ratio of the number of ions, produced in the testing vessel, by an α particle from C compared with that from an α particle emitted by A.
It will be seen later that, for this particular case, K is nearly unity. Taking K = 1, the activity at any time after removal is proportional to λ_{1}P + λ_{3}R.
Case 1. We shall first consider the activity curve for a short exposure to the radium emanation. The relative values of P, Q, and R at any time corresponding to this case are graphically shown in Fig. 74. The activity measured by the α rays at any time will be the sum of the activities due to A and C separately.
Let curve AA (Fig. 74) represent the activity due to A. This decreases exponentially, falling to half value in 3 minutes. In order to show the small activity due to C clearly in the Figure, the activity due to A is plotted after an interval of 6 minutes, when the activity has been reduced to 25 per cent. of its maximum
