To the writer's knowledge there is at present no appreciable evidence that the phenomena connected with the loss of energy by β-particles (and α-particles) in traversing matter, receive any better explanation from the quantum theory than they do from the classical theory. Indeed since precious discussions of the application of the quantum theory in this field are confined to the average rate of loss of energy they cannot possibly support or discredit the quantum theory any more than they do the classical theory, because as regards this effect the two theories have nearly the same requirements. The fundamental difference between the two theories is manifested not in the actual energy lost in travelling a given distance, but in the distribution of this loss of energy between different kinds of collisions.
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E. J. Williams (1931) studied this question.