550 Dr. "W. F. G. Swann on the Pulse 



100 volts, we find g> = 10~ 10 erg. Taking the case o£ photo- 

 electric electrons for which v= say 5xl0 7 , we find that 

 the necessary value of p is 80. Using this value we find 



u 1 

 from (27) that - =-—, which is just about of the right 



order of magnitude for photoelectric effects. Greater values 



of oy would of course correspond to greater values of - . It 



may be mentioned that for X rays where v is of the order 



6 X 10 9 , - would become equal to unity for p = 5, and for 



large values of p, u would completely mask v, as we pointed 

 out on p. 546*. 



So far in the present problem it has not been necessary to 

 introduce the idea of the Planck unit ; if, however, we do 

 so at this stage we arrive at conclusions which though rather 

 speculative are nevertheless interesting. Suppose we con- 

 sider E the total energy which the atom absorbs before the 

 electron is allowed to escape as equivalent to N Planck 



2hNn 

 units, so that from (29) v 2 = , where li is Planck's 



v y mp 



constant. If v 2 is to be proportional to the frequency n we 

 must have p independent of n. Using (25) in conjunction 

 with the expression for the energy per c.c, Ave find, if a is 

 the cross-sectional area of the pulse, since p\a is the volume 

 of the p wave-lengths, 



e 2 U e 2 U 



v 2 = 27rp\ 2 -r 2 ^-=2tt\— 2 — 3 . . . (30) 



1 m p\a m* a ' v y 



where U is the total energy in the p wave-lengths of the 

 pulse. 



If the diameter of the pulse is to be such that the whole 

 of the energy of the p wave-lengths is to be absorbed, we 

 must have E = U. As a matter of fact, since the energy 

 absorbed per oscillation is proportional to the number of the 

 oscillations, in order that the pth wave-length shall have 

 enough energy we must have U = 2E, so that since from (29) 



E= —f- v 2 we find that on substituting in (30) 



2ttX^ 2 p 



a = 



m 



(31) 



* Of course it is not necessary for the application of the theory to 

 X rays that u should mask v. 



