Maximum Frequency of X Rays from a Coolidge Tube, 357 



This limit is probably determined by the characteristic 

 radiation of highest frequency which exists in the atom. 

 Since radium C has an atomic number 83 and uranium — the 

 heaviest known element — 92, we should anticipate from 

 Moseley's relation that the shortest wave-length to be 

 obtained with a uranium anticathode in a vacuum-tube is 

 X = l'40xl0" 9 . The penetrating power of this radiation 

 in aluminium should be fju— "23 instead of = *39 from the 

 Coolidge tube. Under possible laboratory conditions, it thus 

 appears very improbable that we can obtain Xrays as pene- 

 trating as the gamma rays from radium C. 



The Excitation of X rays and the Quantum Theory. 



We have seen that for the Coolidge tube the connexion 

 between the maximum frequency v and the energy E of the 

 exciting electron is given by 



hv = E-cW 

 or 



where v is the frequency to be expected on Planck's theory 

 if the whole energy of the electron is transferred into radia- 

 tion ; V the voltage ; c and k are constants. These formulae 



do not hold beyond the maximum frequency given by E= — , 



1 

 V= 57. If V is expressed in volts, the value of k is 



1/285000. If this formula holds for lower voltages than 

 those actually examined, it is seen that the value of v 

 becomes more nearly equal to v the lower the voltage. The 

 formula suggests that, for a heavy atom like tungsten, the 

 frequency excited by low voltages should very closely agree 

 with that expected on the quantum theory, supposing that 

 the whole energy of the electron is transformed into that of 

 the X ray. It thus appears probable that the simple quantum 

 theory holds for excitation if the voltage is sufficiently small, 

 but that a large correction is required for high voltages. 



It will be of very great interest to examine the correspond- 

 ing relations between frequency and voltage for lighter 

 atoms, and to test whether such a simple relation as that 

 found for tungsten holds in such cases. It is to be anti- 

 cipated that the maximum frequency would be reached for a 

 voltage which diminishes in value as the atomic weight or 

 atomic number decreases. There is one point, however, in 

 this connexion that should be mentioned. We have seen that 

 the maximum frequency obtainable from tungsten is about 



