Theory of X Rays and Photoelectric Rays. 551 



Since p is to be independent of X, (31) requires that a shall 

 be proportional to X. Taking the value of p which we have 

 chosen in the example above, we find a = 8'4 x 10 _11 X, so 

 that for \=2 x 10~~ 5 we find a=17 X 10 -16 , corresponding to 

 a diameter of 4 x 10~ 8 cm.* In the present case each electron 

 requires about 10~ 10 erg to set it free. Even if 10 10 electrons 

 were emitted per second, which would correspond to a photo- 

 electric current of 10~ 10 c.g.s. unit, the actual energy re- 

 quired from the source of light would be only 1 erg per 

 second, so that if we imagine 100 ergs to be supplied from 

 the source per second in the form of ultra-violet energy, we 

 could afford to widen the cross-sectional area of the pulse 

 100 times, so that the diameter would be of the order 



IX 10~ 7 cm. In fact the extreme narrowness of the pulses 

 is not necessitated so much by energy considerations as by 

 the fact that so few electrons are liberated, thou oh there are 

 other ways of accounting for this, e. g. by considering that 

 only a comparatively small number of atoms contain electrons 

 of the appropriate frequencies. 



It must be pointed out that since from (26) and (28) 



E 



u— — independently of the value of p, while from (29) 



2E 



v 2 = — , even in the case of photoelectric effects we can 



mp l 



make u represent the whole of the velocity of the ejected 

 electron, provided that we admit a sufficiently large value of 

 E (a value of the order corresponding to a fall of the ionic 

 charge through 1000 volts). It will be seen that this is so. 

 since by taking a sufficiently large value of p, v 2 becomes 

 reduced to insignificance. Postulating a large value ot p 

 is equivalent to assuming a small value for the energy 

 density, as maybe seen from (26); it is also equivalent to 

 assuming a large value of a, as may be seen from (31). 

 Indeed, if p were iO 15 , a would be about 1 sq. cm., but the 

 pulse would then take about a second to pass, and there are 

 other objections to such large values of p, as may be seen 

 from a consideration of problem 1 in the Appendix. 



It is an interesting point in connexion with the pulses, 



* It can be shown from (28) that in virtue of the constancy of p, 

 Y 2 and consequently the energy-density is proportional to the cube of 

 the frequency. It is interesting to notice, that if we associate hard 



X rays with large densities, they must correspond to high frequencies, 

 and consequently to high velocities for the electrons emitted, with the 

 result that there will be but little scattering. It is a significant fact 

 that the electrons ejected by hard X rays show a much greater want of 

 symmetry than those ejected by soft rays. 



