Theory of X. Rays and Photoelectric Rays. 515 



energy which the electron must have in order to get away, 

 directly E becomes equal to &) the electron will escape. 



We may picture the electron at the beginning of its 

 (p — l)th oscillation with just too little energy to get away. 

 At the pth oscillation it will get away carrying with it the 

 extra amount o£ energy which it obtained in the pth. oscilla- 

 tion, or rather as much of it as was left over after paying 

 the extra little bit necessary to make the energy of the 

 (p — l)th oscillation up to the amount o>. 



If u and v are the average values of x and y with which. 

 the electron is shot out of the atom, the value of \v? is thu& 



of the order — times the energy given to the electron in 



the pth oscillation, while u is - times the much larger 



1 G 



quantity representing — times the total energy, kinetic and 



potential, given to the electron in the p oscillations. In 

 fact, if co is sufficiently large, u may, as we shall see, be 

 greater than v. It may even mask v entirely so that the 

 whole velocity of the ejected electron is in the x direction, 



bemo- given bv u = — 

 ° ** J mc 



If we imagine that the electron absorbs one Planck unit 

 of energy before it escapes, we shall have at=6'o x 10 -27 c/\ % 

 and since m=10~ 27 we have 



(v5 

 «=™ (16) 



If \ = 2xl0~ 5 cm., as for example in the case of ultra- 

 violet light, we find m=3x10 5 , which is much smaller than 

 the velocity of photoelectric electrons, We might rectify 

 this difficulty by imagining that in the case of photoelectric- 

 electrons ft) corresponds not to a single Planck unit, but to 

 N such units, N being approximately the same for all atoms,, 

 but we shall find that for values of X as large as 2 x 10~° there- 

 are difficulties in the assumptions necessary to insure that u 

 is large compared with v, and moreover in this case (16) corre- 

 sponds to too great an asymmetry for photoelectric electrons, 

 so that tempting as the formula is, in that it shows the-; 

 velocity to be proportional to the frequency, I think that we 

 can hardly reconcile ourselves to the belief that it contains, 

 the true explanation of the photoelectric effect. Perhaps, 

 after all this is no matter for great regret in view of the 

 fact that modern measurements seem to show that the maxi- 

 mum velocity is not proportional to the frequency at all, but: 



Phil Mag. S. 6. Yol. 25. No. 148. April 1913, 2 P 



