﻿Distribution of Electrons in Na and CI Atoms. 445 



10 electrons, two are supposed to describe circular one- 

 quantum orbits about the nucleus, while, of the remaining* 

 eight, four describe two-quantum circular orbits and four 

 two-quantum elliptical orbits. We have calculated the size 

 of these orbits from the quantum relation ship and the 

 charges ; this can only be done very approximately, owing 

 to the impossibility of allowing for the interaction of the 

 electrons. We take the following numbers : — 



Radius of 1 quantum ring 0*05 A. 



2 „ 0-34 „ 



Semi-major axis of ellipses * ... 0*42 ,, 



To get a rough idea of the diffracting power of such an 

 atom, we suppose, first, that the orientation of the orbits is 

 random so that the average atom has a spherical symmetry, 

 and also that the periods of the electrons in their orbits are 

 so large compared with the period of the X-rays that we 

 need not consider the effect of their movements. 



The calculation of the effect of the circular orbits offers 

 no difficulties. To allow for the effect of ihe ellipses, the- 

 following method was used. The elliptical orbit was divided 

 into four segments, through each of which the electron would 

 travel in equal times. It was then assumed that, on the 

 average, one of the four electrons describing ellipses would 

 be in the middle of one of these segments. This gives four 

 different values of the radius vector, corresponding in the 

 average atom to four spherical shells of these radii. 



AYe thus calculate the value of F for an atom having 



2 electrons on a shell of radius 0*05 A. IT. 



4 .. „ „ 0-34 ., 



1 „ „ „ 0-27 „ 



1 .. „ „ 0-55 „ 



1 „ „ „ 0-70 „ 



1 n .<, » 0*78 ,, 



* The elliptical two-quantum orbit of a single electron about the 

 sodium nucleus would have a semi-major axis equal to the radius of 

 the two-quantum circle. We have used the larger value 0-42 to make 

 some allowance for the fact that part of the orbit lies outside the inner 

 electrons, so that the effective nuclear charge is reduced. 



