December 17, 1915] 



SCIENCE 



853 



origin in the disintegration of a single 

 atom, or in other words, that each chang- 

 ing atom gave rise to a single a-particle. 

 If this assumption were correct, then an 

 estimate of the total number of a-particles 

 emitted by any radioactive substance would 

 afford a basis for judging as to the number 

 of atoms which underwent transformation 

 in any given period. From the results of 

 experiments by Wien on the number- of 

 /^-particles projected from one gram of 

 radium bromide, and from considerations 

 based on the ionization produced in a gas 

 by the a-particles emitted by a known quan- 

 tity of radium, Rutherford reached the 

 conclusion that one gram of pure radium 

 element expelled 2.5 X 10^" a-particles per 

 second. From data based on experimental 

 evidence it was assumed that the number of 

 molecules in one cubic centimeter of 

 hydrogen at standard pressure and temper- 

 ature was 3.6 X 10^". Taking the atomic 

 weight of radium as 225 it was then calcu- 

 lated that there were 1.8 X 10^^ atoms in 

 1 gram of radium.^ 



If the total number of atoms present was 

 1.8 X 10^^ and the number transformed per 

 second was 2.5 X 10^°, then the fraction of 

 the whole undergoing change per second 

 would be 1.4 X 10"", and per year 4.4 X 

 10"*. This indicated that the half -value pe- 

 riod of radium was about 1,500 years.^ 



Another estimate of the life of radium 

 was made by Rutherford in the Bakerian 

 lecture delivered before the Royal Society 

 in May, 1904. Assuming that the heating 

 effect, which had been observed and meas- 

 ured by P. Curie in radium salts, was due 

 to the bombardment of the salt by the 

 a-particles emitted from the radium which 

 it contained and concluding that heat 



1 An error was made in this calculation, and the 

 correct number based on the data used should have 

 been 3.6 X 10^'. This would have given 3,000 years 

 for the half -value period. 



2 See preceding footnote. 



energy which appeared was derived from 

 the kinetic energy of the moving a-particles, 

 Rutherford calculated the kinetic energy 

 of a single a-partiele on the basis of the 

 data then available. This he found to be 

 6 X 10"° erg per second. The heating effect 

 of about 100 gram calories per hour ob- 

 served for one gram of radium corre- 

 sponded to 1.2 X 10° erg per second. Con- 

 sidering the radium salt as containing four 

 a-ray products (Ra, Ra Em, Ra A and 

 RaC) and assuming an equal distribution 

 of the heating effect between these, it there- 

 fore appeared that the number of a-par- 

 ticles expelled per second per gram of 

 radium itself (and therefore the number of 

 atoms of radium breaking up per second) 

 was 5 X 10^". Applying the same line of 

 reasoning as had been used in the first in- 

 stance for deriving the number of atoms in 

 one gram of radium, Rutherford obtained 

 the value of 800 years for the half -value 

 period of radium.' 



In the year 1905 Rutherford* performed 

 an experiment in which the electrical charge 

 carried by the a-particles from a known 

 quantity of radium was measured. This 

 was found to be equivalent to 4.07 X 10"' 

 ampere per second for the particles emitted 

 by one gram of radium. Assuming the 

 charge on each particle to be the same in 

 value but opposite in sign to the charge car- 

 ried by a single electron; viz., 1.13 X 10"" 

 coulomb, this gave the number of a-par- 

 ticles per second from one gram of radium 

 as 6.2 X 10^°. Estimating, in this case 

 without the previous error, the number of 

 atoms in one gram of radium as 3.6 X 10^^, 

 the value obtained for the rate of change of 

 radium corresponds to a half-value period 

 of about 1,300 years. 



A new and more accurate determination 



3 The error mentioned previously was repeated 

 here, and the correct value given by this calculation 

 is not 800, but 1,600 years. 



i Phil. Mag., 10, p. 193. 



