﻿652 Dr. L. Vegard on the Series Spectrum of 



1 e 

 magnetic moment M^= o vrA 6 an( * tne kinetic energy ^[ico*. 



If the mass of the nucleus is of purely electromagnetic 



2 e 2 

 origin, its radius is equal to ~ ^p when the charge is supposed 



to be on the surface o£ the nucleus. For a volume distri- 

 bution we can assume the formula to give a radius of the 

 right order, or about 10 _16 cm. for the hydrogen nucleus. 

 In order to get a magnetic moment o£ 5 magnetons we 



should have to assume an angular momentum of 1800 — > 



to 2-7T 



and the number of rotations (v) in unit time would be 

 4*6 X 10 31 , and the kinetic energy 2*8 xl0 +8 erg, or about 

 10 19 times the energy of the outer electron in the normal 

 state of the atom. As long as we know so little about the 

 interior of the atom we are perhaps not allowed to say that 

 the existence of such rotations and the enormous store of 

 energy are impossible, although there seems no special reason 

 for the assumption unless we would suppose that the internal 

 energy of the atom which is brought to light through the 

 atomic disintegration is to be of a rotational nature, and that 

 the rotations are preserved also for the lighter elements like 

 hydrogen. 



Let us next consider the case in which the inner magnetic 

 system is composed of (N — 1) electrons circulating round 

 the nucleus with a positive charge -f-N<?. I£ the angular 



N-l ft 



momentum of all inner electrons % ma^co. is equal to x— > 



1 % % LIT 



they would produce a magnetic moment of 5 magnetons. 

 Let all electrons form one ring, then 



a 

 4j = 



(N-lAN-iSN-,) 

 and W,-= (N- JS N -i) 8 (N - 1) 3 W. 



«j and Wt are radius and energy of inner ring, a and W 

 the corresponding quantities for the light-emitting electron 

 in the normal state. 



In order that the inner system shall act electrically on 



the outer electron as a single charge +e, — must be a small 



a- ' a 



quantity. In fact, — diminishes rapidly with increase of N. 



a a- 



Thus with an inner ring of 1 electrons — = 61. and W .= 940 W, 



a 

 * It is supposed that the inner nucleus can be treated as a charged solid 



body. 



