Maximum Frequency of X Rays from a Coolidge Tube. 353 



is so widely departed from in excitation of X-rays by swift 

 electrons, bnt at present we shall consider' whether there is 

 any simple relation between frequency and voltage. The 

 frequency curve is approximately parabolic in shape and can 



M 









Fig. 5. 











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1 /I 



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1 / 1 ! 









1 ' i ~7^ 





c 1 

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_L I' VyAt' 





X-— ^ o 



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40 60 8C 100 120 W0 ICO 190 



Voltage in thousands. 



be expressed by the relation v = aN — b\ 2 , where a and b are 

 constants and V is the voltage. This relation can be put into 

 a simpler form, viz., 



/ t v = E-cE 2 , (1) 



where E is the energy of the electron moving through 

 a difference of potential E and c a constant. Planck's 



relation held for excitation, E 

 lated frequency 

 simple form 



where v p is the calcu- 



It is seen that the relation reduces to the 

 rA-.-1-JbV; 



By differentiating equation (1), it is seen that the frequency 

 v reaches a maximum when E = l/2c or Y—l/2k. 



If V is expressed in volts, the value of 1/k which fits the 

 results best is 285,000 volts. The frequency reaches a 

 maximum at half this voltage, or at 142,500 volts. 



Phil. Mag. S. 6. Vol. 30. No. 177. Sept. 1915. 2 A 



