| 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 λ1P + λ3R. The activity measured by the α rays, using the electrical method, is thus proportional at any time to λ1P + Kλ3R, 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 λ1P + λ3R.
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 value. The activity due to C is proportional to λ3R, and in order to represent the activity due to C to the same scale as A, it is necessary to reduce the scale of the ordinates of curve CC in [Fig. 72] in the ratio λ3/λ1.
Fig. 74.
The activity due to C is thus represented by the curve CCC, [Fig. 74]. The total activity is thus represented by a curve A + C whose ordinates are the sum of the ordinates of A and C.
This theoretical activity curve is seen to be very similar in its general features to the experimental curve shown in [Fig. 66], where the activity from a very short exposure is measured by the α rays.