Structure of the Atom. 263 



I£ now we write 



-^ma) n 2 r n 2 ^qhv n , 



where li is Planck's constant and q is a numerical multiplier, 

 we find * 



1 27r 2 mC /l _1\ 



r 2 ^ qh \}h 2 VnY 



In Balmer's series jc 1 = 2 and the least value of p n is 3. 

 Thus the minimum value o£ r from which bright line 

 radiation arises is 



7T V «C 



and the maximum value is 3/^/5 times larger. With 

 the data A=6'5 (10)" 27 , m=8'8 (lO)" 28 , C = 3-3 (10) 15 , we 

 get as the minimum and maximum value respectively, on 

 the assumption g=l, the numbers 2*13 (10) ~ 8 cm. and 

 2'86(10)~ 8 cm., which are quite in accordance with estimates 

 of molecular magnitudes. The maximum is only twice as 

 great as the value deduced for hydrogen from the observed 

 density in the liquid state. Agreement would result if 



It is of interest to consider conditions under which the 

 value q=l/2 would hold. If we write 



mco n 2 r n =k n r n e 



J moon 2 r 2 = 2tt 2 mv 2 r n 2 = qliv m 

 we find 



, q 2 h 2 1 



Thus the attraction within each region n, of small breadth 

 fn'—fni is the attraction due to the law of the inverse cube 

 of the distance from the centre of the atom. If this law is 

 identical with the law of repulsion in the other regions we 

 get 



"72 



TT z me 

 If now we also have 



mw a r 2 = a } 



i, e. if angular momentum is conserved in the regions n, we 



get 



2 o 7 2 <f h ' 2 



<r = >mahvn r<s = — .j 



1 7T- 



