2 compton: size and shape of electrons 



such as the production of secondary photoelectrons or beta rays, 

 and for other than waves of short length the rays scattered by 

 the different electrons in an atom are nearly enough in the 

 same phase to produce the phenomenon of ''excess scattering," 

 so that the absorption coefficient is in most cases considerably 

 greater than the value given by this expression. If the electron 

 acts as a point charge there is, however, no possible grouping 

 of the electrons which can, according to classical theory, produce 

 a smaller absorption than that calculated according to Thomson's 

 formula. 



Barkla and Dunlop^ have shown that for a considerable range 

 of wave-lengths of X-rays the mass scattering coefficients of the 

 lighter elements are given accurately by equation (1) if the 

 number of electrons in the atom is taken to be approximately 

 half the atomic weight. For elements of high atomic weight the 

 phenomenon of excess scattering occurs, except with the very 

 shortest wave-lengths, and the absorption coefficient due to 

 scattering becomes much greater than this value. For wave- 

 lengths less than 2 X 10 ~^ cm., however, the absorption co- 

 efficient becomes very appreciably less than that theoretically 

 calculated, falling as low as one-fifth as great for the shortest 

 7-rays. Soddy and RusselP and Ishino* have shown that for 

 these shortest rays the amount of energy scattered by the dif- 

 ferent elements is accurately proportional to their atomic num- 

 bers, so that all the electrons outside the nucleus are effective 

 in producing absorption. It is therefore impossible to account 

 for this very considerable decrease in the absorption coefficient 

 for very short electromagnetic waves if the electron is considered 

 to be a point charge of electricity. 



If, however, the diameter of the electron is comparable in 

 magnitude with the wave-length of the incident wave, the ra- 

 diation scattered by different parts of the electron will be so 

 different in phase that the energy of the scattered rays will be 

 materially reduced. If, for example, the charge on an electron 



^ Barkla and Dunlop. Phil. Mag., March, 1916. 



3 Soddy and Russell. Phil. Mag. 18: 620. 1910; 19: 725. 1910. 



^IsHiNO. Phil. Mag. 33: 129. 1917. 



