366 Sir E. Rutherford and Prof. J. Barnes on Efficiency 



On the latest data *, the initial energy of the alpha particle 

 from radium C is 7*66 x 10 14 £, where e is the charge on the 

 ions in electromagnetic units. From this it can be deduced that 

 the energy required to produce a pair of ions in air is equal 

 to the energy acquired by the unit charge in moving freely 

 through a potential difference of 33 volts. If % x is the total 

 ionization current and i 2 the electronic current 



efficiency = X " ray energy - 1 } V , ' 

 cathode-ray energy t a V 



where u=33 volts and Y = the voltage applied to the tube. 



Yoltoge. 



Ratio, 



Efficiency. 



P 2 . 



Efficiency//} 2 . 



48,000 



•86 



•o9xl0" 3 



•165 



3-6 



64,000 



1-44 



•74 „ 



•211 



35 



96,000 



3-01 



1-04 „ 



•292 



3-6 



The efficiency deduced in the above table is for ordinary 

 working conditions when no correction is made for absorption 

 in the glass walls, &c. Under these limitations, the efficiency 

 is seen to be proportional to /3 2 . No doubt the closeness of 

 the agreement is accidental, for the numbers would be changed 

 if corrections were made for absorption of the radiation. 



We have seen earlier that about half the energy of the 

 radiation is probably absorbed in the bulb. We should 

 consequently expect the efficiency under ideal conditions to 

 be about 1/500 for 96,000 volts, and 1/800 for 48,000 volts. 

 It is of interest to note that Wien (loc. cit.) found an efficiency 

 of 1*09 X 10 -3 for a platinum anticathode, using a bolometer 

 method to measure the energy of the X rays for a potential 

 of 58,700 volts supplied by an induction-coil. Since the 

 average potential of the discharge due to an induction-coil is 

 less than the maximum, it is to be expected that the efficiency 

 of the coil would be somewhat higher than for an equal steady 

 voltage supplied by a machine. 



Beatty (loc. cit.) found the efficiency to be given by 



E = 2-54xl0" 4 A/3 2 . 

 The value of the numerical factor involves the average 

 energy required to produce a pair of ions. This was deduced 

 by a very indirect method by a combination of distinct in- 

 vestigations by Glasson and Whiddington. From the data 



* Rutherford and Robinson, Phil. Mag. xxviii. p. 551 (1914). 



