403 



potential enei-gy of the formed products is greater tliaii that of the 

 atoms before the decomposition, so that this increase of potential 

 energj' too would have to be accounted for by the zero-point energy. 



Such a supposition of particles moving with great velocity in the 

 radio-active atom has been made already before. But considered 

 without connection with the zero-point energy it seemed too arbitrary, 

 and Hahn and Mkitner's and von Bayer's experiments, which showed 

 that the /J-rays of a certain radio-active atom are homogeneous, 

 seemed to point to a definite loss of potential energy of the emitted 

 particles, which was found back in the form of kinetic energy^). 

 This homogeneity of the rays, however, might now be explained in 

 a different way, \'iz. by assuming that a particle tiiat vibrates with 

 a period v in the atom, is also emitted with an energy vh. Then 

 there would be a close correspondence between radio-activity and 

 the light-electric effect. The difference between the two phenomena 

 would only consist in this, that for tlie latter light falling on the 

 atom from the outside, for the former cooperation of the different 

 intra-atomic motions gave rise to the emission. 



According to this supposition the frequency of the internal vibrations 

 for /?-rays emitted with a velocity v = 0,92 c. would have to be 

 estimated at v = 8,25 X J0'^ 



SoMMERFELD ') Calculates A r= 6 y; 10—^^ for the y-rays with this 

 velocity of the H-rays, which corresponds to u = 5 X lO—-'^. Hence 

 the period of the internal vibrations according to this supposition 

 would have to be somewhat greater than corresponds with the 

 wavelength of the coi-responding y-rays. At any rate the value which 

 we find in this way for the frequency is so great that even at the 

 highest temperatures attainable we are very far from the point at 

 which, according to Planck's formula, we could expect any perceptible 

 change in the energy of the motions, so that the otherwise so un- 

 accountable fact that not the slightest influence of the temperature 

 is found on the radio-active phenomena is very satisfactorily interpreted. 



Perhaps little weight should be attached to such not quantitatively 

 testable considerations. I myself also doubt whether they supply a 

 sufficient ground to justify us in adopting a zero-point energy in 

 spite of the difficulties which attend it. Yet I have thought I ought 

 to point out the advantages whicli it offers. 



1) It is perhaps also possible to retain this view, and only acid to it the 

 assumption that, in order to be able to be emitted, a particle must beforehand 

 have been brought by the zero-point motion in such a position of maximum 

 potential energy that it is shot out from there with that definite energy. 



3) SoMMERFELD. Gougrcs Solvay, 1911, p. 342. 



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