Page:Radio-active substances.djvu/81

then been removed from the enclosure, parts with its activity in free air according to an exponential law, which is the same for all bodies represented by the following formula:—

${\text{I}}={\text{I}}_{0}\left(ae^{-{\frac {t}{\theta _{1}}}}-\left(a-1\right)e^{-{\frac {t}{\theta _{2}}}}\right).$

${\text{I}}_{0}$ being the initial intensity of the radiation at the moment of withdrawing the plate from the enclosure; ${\text{I}}$, the intensity after time, $t$; $a$ is a numerical coefficient, $a$ = 4·20; $\theta _{1}$ and $\theta _{2}$ are time constants, $\theta _{1}$ = 2420 secs., $\theta _{2}$ = 1860 secs. After two or three hours this law becomes practically a simple exponential, and the effect of the second exponential upon the value of I is negligible. The law of dissipation is therefore such that the intensity of radiation becomes diminished to one-half its value in twenty-eight minutes. This final law may be considered as characteristic for the dissipation in an unconfined air space of the activity induced in solid bodies by radium.

Solid bodies excited by actinium lose their activity in the open air, according to an exponential law similar to the preceding, the dissipation being, however, rather slower. Solid bodies, made active by thorium, lose their activity much more slowly; the intensity of the radiation is reduced to one-half in eleven hours.

 

Dissipation of Activity in a Confined Space.
Velocity of Destruction of the Emanation.

An enclosure, made active by radium and then removed from its influence, loses its activity by a law which is much less rapid than that of dissipation in the open air. The experiment may be carried out with a glass tube, rendered active internally by placing it for some time in contact with a solution of a salt of radium. The tube is then sealed in the flame, and the intensity of radiation emitted by the walls of the tube is measured while the dissipation takes place.

The law of dissipation is an exponential law. It is given very accurately by the formula.

${\text{I}}={\text{I}}_{0}e^{\frac {t}{\theta }}.$

${\text{I}}_{0}$ = initial intensity of radiation.
${\text{I}}$ = intensity of radiation at time, $t$,
$\theta$ = a time constant, $\theta =$4·970 $\times 10^{5}$ secs.

The intensity of the radiation is reduced to one-half in four days.

This law of dissipation is absolutely invariable whatever be the experimental conditions (dimensions of enclosure, nature of the walls, nature of the gas within the enclosure,