﻿L 433 ] 



XLIII. The Distribution of Electrons around the Nucleus in the 

 Sod/ ion and Chlomne Atoms. By W. Lawren'CE Bragg, 

 M.A., T.lx.S.. Langworthy Professor of Physics, The 

 University of Manchester ; R. W. James, M.A., Senior 

 Lecturer in Physics, The University of Manchester ; and 

 C. H. Bosanquet, M. A., Balliol College, Oxford*. 



1. TN two recent papers f in the Philosophical Magazine 

 i the authors have published the results of measure- 

 ments made on the intensity of: reflexion of X-rays by 

 rock-salt. The mathematical formula for the intensity of 

 reflexion, as calculated by Darwin J, involves as one of 

 its factors the amount of radiant energy scattered in various 

 directions by a single atom when X-rays of given amplitude 

 fall upon it. The other factors in the formula can bo 

 evaluated. By measuring the intensity of reflexion experi- 

 mentally we can therefore obtain an absolute measurement 

 of the amplitude of the wave, scattered by a single atom, 

 in terms of the amplitude of the incident radiation. 



This measurement is of considerable interest, because it 

 may throw some light on the distribution of the electrons 

 around the nucleus of the atom. We regard the wave scat- 

 tered by the atom, as a whole, as the resultant of a number of 

 waves, each scattered independently by the electrons in the 

 atom. A formula first evaluated by J. J. Thomson is used 

 in order to calculate the amplitude of the wave scattered by 

 a single electron. If an incident beam of plane polarized 

 X-rays consists of waves of amplitude A, then the amplitude 

 A' at a distance R from the electron in a plane containing 

 the direction of the incident radiation, and at right angles 

 to the electric displacement, is given by 



A R mc 2 {) 



Here e and m are the charge anc [ m ass of the electron in 

 electromagnetic units, and c is the velocity of light. 



What we measure experimentally is the resultant ampli- 

 tude of the wave-train scattered in various directions by a 

 number Z of electrons in the atom. If all the electrons were 



* Communicated by the Authors. 



t Phil. Mag. vol. xli. March 1921 ; vol. xlii. July 1921. 

 X C. G. Darwin, Phil. Mag. vol. xxvii. pp. 315-675 (Feb. and April 

 1914). 



Phil. Mag. S. 6. Vol. 44. No. 261. Sept. 1922. 2 F 



