221. Analysis of the β-ray curves. The analysis of the changes is much simplified by temporarily disregarding the first 3-minute change. In the course of 6 minutes after removal, three quarters of the matter A has been transformed into B and 20 minutes after removal all but 1 per cent. has been transformed. The variation of the amount of matter B or C present at any time agrees more closely with the theory, if the first change is disregarded altogether. A discussion of this important point is given later ([section 228]).
The explanation of the β-ray curves (see Figs. [87] and [88]), obtained for different times of exposure, will be first considered. For a very short exposure, the activity measured by the β rays is small at first, passes through a maximum about 36 minutes later, and then decays steadily with the time.
The curve shown in [Fig. 87] is very similar in general shape to the corresponding thorium and actinium curves. It is thus necessary to suppose that the change of the matter B into C does not give rise to β rays, while the change of C into D does. In such a case the activity (measured by the β rays) is proportional to the amount of C present. Disregarding the first rapid change, the activity It at any time t should be given by an equation of the same form ([section 207]) as for thorium and actinium, viz.,
where IT is the maximum activity observed, which is reached after an interval T. Since the activity finally decays according to an exponential law (half value in 28 minutes), one of the values of λ is equal to 4·13 × 10-4. As in the case of thorium and actinium, the experimental curves do not allow us to settle whether this value of λ is to be given to λ2 or λ3. From other data (see [section 226]) it will be shown later that it must refer to λ3. Thus λ3 = 4·13 × 10-4 (sec)-1.
The experimental curve agrees very closely with theory if λ2 = 5·38 × 10-4 (sec)-1.
The agreement between theory and experiment is shown by the table given below. The maximum value IT (which is taken as 100) is reached at a time T = 36 minutes.
In order to obtain the β-ray curve, the following procedure was adopted. A layer of thin aluminium was placed inside a glass tube, which was then exhausted. A large quantity of radium emanation was then suddenly introduced by opening a stop-cock communicating with the emanation vessel, which was at atmospheric pressure. The emanation was left in the tube for 1·5 minutes and then was rapidly swept out by a current of air. The aluminium was then removed and was placed under an electroscope, such as is shown in [Fig. 12]. The α rays from the aluminium were cut off by an interposed screen of aluminium ·1 mm. thick. The time was reckoned from a period of 45 seconds after the introduction of the emanation.
| Time in minutes | Theoretical value of activity | Observed value of activity |
|---|---|---|
| 0 | 0 | 0 |
| 10 | 58·1 | 55 |
| 20 | 88·6 | 86 |
| 30 | 97·3 | 97 |
| 36 | 100 | 100 |
| 40 | 99·8 | 99·5 |
| 50 | 93·4 | 92 |
| 60 | 83·4 | 82 |
| 80 | 63·7 | 61·5 |
| 100 | 44·8 | 42·5 |
| 120 | 30·8 | 29 |
There is thus a good agreement between the calculated and observed values of the activity measured by the β rays.