532 SCIENCE PROGRESS 



logarithmic or exponential curves correspond to an equation 

 of the type — 



Y; = ^-^^ (I). 



In the case under consideration L is the initial activity of 

 thorium X, I/-the activity after time /, \ is a constant, and e the 

 natural base of logarithms (= 27183 .. .)• 



The recovery curve is the inverse of this curve, and is 

 represented by the equation — 



l'=i-^-^' .... (2), 



la 



where I^ is the final activity (the maximum figure obtained), 

 I, the activity recovered after time t, and \ is the same constant 

 as in the previous equation. 



These results have been given in some detail because they 

 are typical of most of the curves obtained by plotting the 

 change of activity against time. In all cases the decay curve 

 of the radioactive child bears the relation to its radioactive 

 parent that the constant X is the same for the two cases. The 

 curves illustrate two further points. They approach constant 

 value towards the end of a month, but it is seen that they 

 reach a final value only at infinite time. This property is 

 common to all such curves ; it illustrates the fact that the 

 life of a radioactive element is infinite. In order to compare 

 such lives we therefore speak of the half-life period, a definite 

 value for each element. It represents the time in which half 

 the element disintegrates; its activity falls to half value. This 

 time can be calculated graphically from the curves, or from 

 equation (i), since the activity has fallen to half value, L = 2I,, 

 i.e. 2 = ^-"^'. Hence if \ is known, / can be calculated. Again, 

 \ represents the proportion of atoms changing per unit of time ; 

 VA- thus represents the average life of an atom of the element 

 under consideration. A discussion of the meaning of these 

 terms is given in Section 3 (p. 538). In the case of thorium X 

 the half-time is four days. 



Hahn has recently shown that thorium at first disintegrates 

 into mesothorium, and this into radiothorium ; the last named is 

 the immediate parent of thorium X. Radiothorium is very 

 much more active than the thorium from which it is derived. 

 The methods employed were similar to those just described — 



