the Radiations from Radioactive Substances. 21 



The variation of the rate of production of ions from a 

 particle with the time of deposit, is supposed to include the 

 effect of different kinds of radiations emitted, which may 

 also have different rates of decay, and any effects of excited 

 radioactivity on the body on which it is deposited. 



For simplicity, suppose that the radioactive carriers are 

 deposited at a uniform rate of q per second. (This is the 

 case in practice where the amount of emanation present does 

 not vary with the time ) 



The number of ions produced per second after a time t 

 by the radioactive particles deposited for the first short 

 interval of exposure dt is given by 



?"o/(0 dt. 



The number of ions N produced per second by the radio- 

 active matter deposited during the time t is given by 



N = gn V 



/(*)* 



A steady state is reached when the rate of supply of fresh ions 

 per second, by the addition of radioactive material, is equal 

 to the rate of diminution due to decay of excited radiation 

 as a whole. 



This steady state is reached after a long interval of exposure, 

 and the maximum rate of production of ions N is given by 



N =?n I /(0 dt ' 



If the curve of decay of excited radiation due to a single 



N 

 particle is plotted with the ratio -jrp as ordinate and t as 



abscissa, the value of these integrals can at once be obtained. 



The rise of excited radioactivity with time can thus be at 

 once deduced from the decay-curve of a single particle, and 

 vice versa. 



The rate of production of ions Nj due to the excited 

 radiation, after removal for a time t l from the emanation, is 

 given by 



J (0 dt, 



^ l = gr} \ 



where t is the time of exposure. 



