540 Dr. W. F. G. Swann on the Pulse 



about one-hundredth. o£ the diameter of an atom *. The 

 energy in the Planck unit for A- = 5xl0~ 9 cm. amounts to 

 4xl0 -8 erg, and that of the electron is about 2xl0 -8 , so 

 that the electron will take about half the energy of the 

 pulse. 



If we were to imagine a pulse containing a much larger 

 amount of energy but of the same energy density — i. e., a 

 pulse of greater diameter — the same actual amount of energy 

 would be absorbed by the electron, but this energy would 

 then only be a small fraction of the total amount. The real 

 gain in concentrating the energy in a narrow beam is that 

 we then get an appreciable fraction of it absorbed by the 

 electron. This fact is not as obvious as it may at first sight 

 appear, and its reason, as we see, is more deep-seated than 

 can be explained by an attempt to account for it by con- 

 siderations of the relative widths of the pulse and of the 

 electron. 



There is another method in which we may increase the 

 fraction of the energy which is absorbed from the wave- 

 trains without increasing the energy density so much by 

 narrowing the pulses — viz., by splitting the pulses up into a 

 large number carrying altogether the same total amount of 

 energy, but following each other more or less at random, 



with the restriction that at the advancing wave-front < — 



fe da- 



is of the same sign for each pulse. Each of the pulses in 

 passing over the electron communicates an amount of 

 momentum in the y direction, of which the velocity factor is 



Y e\ 

 equal either to zero or to — - — , according as the number of 

 J emir to 



half wave-lengths is even or odd. The average velocity 

 given during the passage of s pulses is thus *~ f . It 



may be noted that this expression is true even if the pulses 

 follow each other so rapidly that they overlap, since it is 

 easy to see that (neglecting the movement of the electron in 

 the x direction during the passage of a single pulse) we may 

 look upon each pulse as producing its own contribution to 

 the y momentum of the electron, independently of the others. 



* If we calculate the distance the electron travels in the y direction 

 by the time y attains its maximum, we shall find it to be 2*5 X 10~ 10 cm., 

 which is rather greater than the width of the pulse ; but to overcome 

 this difficulty it is only necessary to take a rather different value of X, 

 or to assume that the pulse contains more than a single; Planck unit. 



t Similar remarks with regard to damped trains apply as in the last 

 problem. 



