SEPT. 19, 1921 WYCKOFF: WAVE LENGTHS OF X-RAYS 373 



expenditure of a single quantum of energy (n = 1), as would seem 

 probable, then the resulting wave length is in agreement with that 

 calculated from the "sodium chloride arrangement." 



The fact that it is not possible at the present time to obtain the 

 structure of any crystal with surety without at the same time knowing 

 the wave lengths of X-rays would consequently make it seem more 

 logical to think of our determination of the wave lengths of X-rays 

 (and with it all of our studies of the arrangement of the atoms in 

 crystals) as based directly upon this quantum hypothesis, to stand or 

 to fall with it. 



Of course even this determination of the wave length of X-rays is 

 not entirely satisfactory. For instance if, for some reason, it should 

 seem desirable to suppose that the expenditure of two quanta of 

 energy were required to excite X-rays, then we should have a value of 

 the wave lengths corresponding to a structure for sodium chloride 

 having thirty-two chemical molecules associated wdth the unit. Fur- 

 thermore the extension of the quantum relationship from the range 

 of Hght radiation to that of X-rays was indeed a large extrapolation. 

 In spite of this, the most persuasive evidence that a satisfactory deter- 

 mination has been obtained is to be found in the fact that the appli- 

 cation of the quantum relation to the limit of the continuous radia- 

 tion^^ yields values for wave lengths which are in such close accord 

 with a reasonable determination of crystal structure. This structure 

 happens to be the "sodium chloride arrangement" (in the case of sodium 

 chloride) . 



Summary 



Taking the case of sodium chloride as typical, it is shown that there 

 are other structures besides the commonly accepted "sodium chloride 

 arrangement" which are in agreement with the present experimental 

 data. As a result of this lack of definiteness it is emphasized that it is 

 more logical to consider the value of the wave lengths of X-rays as 

 based upon the quantum hypothesis. 



^* E, the energy, can be obtained from a knowledge of the voltage required to produce 

 X-rays of the frequency v and of the charge (e) on the electron ; h is the universal constant 

 of Planck; and n is an integer. 



