206 Prof. E. Butherford on the Charge 



Thus in a gram of radium about half a milligram disintegrates 

 per year. Now it is probable that, as in every other radio- 

 active product, the number of atoms of radium which break 

 up is always proportional to the number present. Thus if n 

 is the number present after an interval t, and n the initial 



n 



number, then — =e~ xt . The value of X is 54 x 10 (year) -1 , 



"o 

 so that the time required for the radium to be half trans- 

 formed is about 1280 years. The average life of radium is 

 thus 1850 years. 



Volume of the Emanation. — Each atom of radium in break- 

 ing up is supposed to produce one atom of emanation. If q 

 is the number of atoms of emanation produced per second 

 per gram, the total number of atoms N present when radio- 

 active equilibrium is reached is given by N = ^, where X is 



X 



the radioactive constant of the emanation. Now q = 6*2 x 10 10 , 

 and 1/X= 480000, thus N = 3'0x 10 16 . 



But one cubic centimetre of any gas contains 3*6 X 10 l& 

 molecules. Thus the maximum volume of the emanation to 

 be obtained from one gram of radium in radioactive equili- 



3*0 x 10 16 

 brium is equal to ^— ; — ^te c.c. = , 83 cubic millimetres. 

 ^ 3bxl0 1J 



Now Ramsay and Soddy found experimentally that the volume 

 of emanation to be obtained from one gram of radium was 

 about one cubic millimetre. The numbers are thus in oood 



o 



agreement. 



Heating Effect of Radium. — Rutherford and Barnes have 

 shown that the heating effect of radium and of its various 

 products is due to the bombardment of the a particles expelled 

 from them. From measurements of the constants of the 

 a. particle, I deduced that its kinetic energy was about 

 5 - 9 x 10~ 6 erg. 



Radium in radioactive equilibrium emits 2 '5 X 10 11 a particles 

 per second per gram. The emission of energy in the form 

 of kinetic energy of the a particles thus corresponds to 126 

 gram-calories per gram per hour. This num ber is in fairly good 

 agreement with the value 100, first determined experimentally 

 by Curie and Laborde. 



If the heating effect of radium is assumed to be a measure 

 of the kinetic energy of the a. particles, we may conversely 

 deduce that the average energy of the a particle emitted from 

 radium and its products is 4'7x 10 -6 erg. 



Number of Ions produced hy an a particle. — Knowing the 

 number of a particles expelled per second from a thin film 



