86 BELL SYSTEM TECHNICAL JOURNAL 



motion of the electron. Momentum also is conserved in the en- 

 counter; the momentum of the quantum is equal in magnitude to 

 hnjc before and to hn'jc after the collision, n and n' standing for the 

 frequency before and after; these momenta are of course vectors 

 parallel to the directions along which the corpuscle of light approaches 

 and recedes, respectively; and their difTerence is the momentum which 

 the electron acquires. These two conditions limit very severely the 

 transfer of energy from quantum to electron. All of the quanta 

 deflected through a given angle from their original line of flight sufifer 

 the same loss of energy and the same shift in frequency. The relation 

 between shift of frequency and angle of deflection d takes its simplest 

 form when we write it as a relation between shift of wave-length, AX, 

 and angle d: 



A\ = — {\ - cos d). 

 mc 



The maximum shift of wave-length occurs when the quantum is re- 

 flected straight backward along its original line of approach; it is 

 evidently Ihjmc, and the corresponding maximum frequency shift is 

 2hn^/mc'\ as I stated earlier. 



The predicted relation of wave-length shift and angle of scattering 

 has been verified to the most thoroughgoing extent; ^^ and the recoiling 

 electrons have been observed as they dash ofi with the energy which 

 the corpuscle of light has lost. Research on the Compton effect is now 

 confined almost entirely to the problem of its likelihood of occurrence — - 

 i.e., given a substance with P atoms per unit volume irradiated by a 

 stream of X-rays composed of N quanta per unit area per second, what 

 are the relations between the number of these quanta which are 

 scattered in the fashion just described, and the frequency of the X-rays 

 and the nature of the atoms? The corresponding problem for the 

 Raman effect will undoubtedly soon come into the foreground. It is, 

 of course, slightly annoying that we do not know a priori how many of 

 the electrons of (say) the carbon atom, or how many of the electrons 

 in a piece of graphite, are to be regarded as "free" electrons. This 

 seems to be one of the facts which we shall have to deduce as best we 

 may from these researches on the likelihood of the Compton effect. 

 The data thus far acquired may be summarized in this way: the higher 

 the frequency of the quanta, and the lower the mass of the atoms, the 

 more abundant these collisions are. High-frequency X-rays poured 



17 Even to the point where with general assent it is taken for granted and the 

 measurements are used as data for evaluating the constant m, the mass of the elec- 

 tron ! 



