Page:Radio-activity.djvu/430

 months afterwards, is λ_{1}n_{0}e^{-λ_{1}t}, and the number of α particles emitted by radium F is

(λ_{1}λ_{2}n_{0}/(λ_{1} - λ_{2}))(e^{-λ_{2}t} - e^{-λ_{1}t}).

The results are shown graphically in Fig. 96, by the curves EE and FF, in which the ordinates represent the number of β and α particles expelled per second by the products D and F respectively. The complete calculation for three changes shows that the number of β particles soon reaches a practical maximum, and then decays nearly exponentially with the time, falling to half value in 40 years. The number of α particles expelled per second increases for several years, but reaches a maximum after 2·6 years and then diminishes, finally falling off exponentially with the time to half value in 40 years.

The experimental curve of the rise of α ray activity, shown in Fig. 93, as far as it has been determined, lies accurately on this curve, if the maximum is calculated from the above theory. The observed activity after a period of 250 days is marked by the point X on the curve.

237. Experiments with old radium. Since the substance radium D is produced from radium at a constant rate, the amount present mixed with the radium will increase with its age. The writer had in his possession a small quantity of impure radium chloride, kindly presented by Professors Elster and Geitel four years before. The amount of radium D present in it was tested in the following way:—The substance was dissolved in water and kept continuously boiling for a period of about six hours. Under these conditions the emanation is removed as rapidly as it is formed, and the β rays from the radium, due to the product radium C, practically disappear. A newly prepared specimen of radium bromide under these conditions retains only a fraction of 1 per cent. of its original β radiation. The old radium, however, showed (immediately after this treatment) an activity measured by the β rays of about 8 per cent. of its original amount. The activity could not be reduced any lower by further boiling or aspiration of air through the solution. This residual β ray activity was due to the product radium E stored up in the radium. The