PRESENT PROBLEMS IN RADIOACTIVITY. 21 



radio-element. The radioactivity of these products is not permanent, 

 but decays according to an exponential law with the time. The 

 activity I at any time t is given by 1 1 = I e ~ M , where I is the initial 

 activity and A a constant. Each radioactive product has a definite 

 change constant which distinguishes it from all other products. These 

 products do not arise simultaneously, but in consequence of a suc- 

 cession of changes in the radio-elements; for example, thorium in 

 breaking up gives rise to Th X, which behaves as a solid substance 

 soluble in ammonia. This in turn breaks up and gives rise to a 

 gaseous product, the thorium emanation. The emanation is again 

 unstable and gives rise to another type of matter which behaves as a 

 solid and is deposited on the surface of the vessel containing the 

 emanation. It was found that the results would be quantitatively ex- 

 plained on the assumption that the activity of any product at any 

 time is the measure of the rate of production of the next product. 

 This is to be expected since the activity of any substance is propor- 

 tional to the number of atoms which break up per second, and, since 

 each atom in breaking up gives rise to one atom of the next product 

 together with a or ft particles, or both, the activity of the parent is a 

 measure of the rate of production of the succeeding product. 



Of these radioactive products, the radium emanation has been 

 very closely studied on account of its existence in the gaseous state. 

 It has been shown to be produced by radium at a constant rate. The 

 amount of emanation stored up in a given mass of radium reaches a 

 maximum value when the rate of supply of fresh emanation balances 

 the rate of change of the emanation present. 



If q be the number of atoms of emanation produced per second 

 by the radium, and N the maximum number present when radioactive 

 equilibrium is reached, then N=q/X, where A. is the constant of change 

 of the emanation. This relation has been verified experimentally. 

 The emanation is found to diffuse through air like gas of heavy molec- 

 ular weight. It is unattacked by chemical reagents and in that re- 

 spect resembles the inert gases of the argon family. It condenses 

 at a definite temperature — 150° C. Its constant of change is un- 

 affected between the limits of temperature of 450° C and — 180° C. 

 Since the emanation changes into a non-volatile type of matter which 

 is deposited on the surface of vessels, it was to be expected that the 

 volume of the emanation would decrease according to the same law 

 as it lost its activity. These deductions based on the theory have been 

 confirmed in a striking manner by the experiments of Eamsay and 

 Soddy. The radium emanation was chemically isolated and found to 

 be a gas which obeys Boyle's law. The volume of the emanation ob- 

 served was of the same order as had been predicted before its separa- 

 tion. The volume was found to decrease with the time according to 



