or
λ2 N2
---- = ---- .
λ1 N1
The ratio N2/N1 was determined by measuring the activity due to the β rays from C and E in the same testing-vessel. Then, since N2/N1 is known, and also the value of λ1, the value of the constant of change, λ2, of radium D is obtained. In this way it was calculated that D is half transformed in about 40 years.
In the above calculations it is assumed, as a first approximation, that the β rays from C and E have the same average velocity. This is probably not accurately the case, but the above number certainly serves to fix the order of magnitude of the period of the product D. This calculation is confirmed by observations to be given later on the amount of D and E in old radium.
It may be of interest to mention that the writer calculated the period of radium F by a similar method, before its value was experimentally determined, and found that F should be half transformed in about one year. This is not very different from the experimental value of 143 days found later. In addition, it was assumed in the calculation that the α particles from C and F were projected with the same velocity, and in consequence produced the same amount of ionization. In practice, however, it is found that the α particle of F is absorbed in about half the distance of the α particles of C, and in consequence produces only about half of the ionization of the latter. If this correction were made, the calculated period for half transformation would be six months instead of one year.
A table of the transformation products of radium, together with some of their physical and chemical properties, is given below.
| Transformation Products | Time to be half transformed | Rays | Chemical and Physical Properties |
|---|---|---|---|
| Radium | 1200 years | α rays | — |
| Emanation | 3·8 days | α rays | Chemically inert gas; condenses at -150° C. |
| Radium A (active deposit of rapid change) | 3 mins. | α rays | Behaves as solid; deposited on the surface of bodies; concentrated on cathode in electric field. Soluble in strong acids; volatile at a white heat. B is more volatile than A or C. |
| :: B (same) | 21 mins. | no rays | Same |
| :: C (same) | 28 mins. | α, β, γ rays | Same |
| :: D (active deposit of slow change) | about 40 years | no rays | Soluble in strong acids and volatized below 1000° C. |
| :: E (same) | 6 days | β (and γ) | Non-volatile at 1000°C. |
| :: F (same) | 143 days | α rays | Volatile at 1000° C; deposited from solution on to bismuth plate. |
| ? | — | — | — |
236. Variation of the activity over long periods of time. We are now in a position to calculate the variation of the α and β ray activity of the active deposit over long periods of time. If it is supposed that the matter initially deposited consists only of D, the amounts P, Q and R of radium D, E and F existing at any later time are given by the equations 3, 4, 5, [section 197].