CONTEMPORARY ADVANCES IN PHYSICS 69 



the spectrum of the scattered light due to a single primary spectrum 

 line consists of that line accompanied by a number of others, separate 

 from it and from one another. Intermediate frequencies do not occur, 

 for they would correspond to transfers of energy in quantities which 

 the atoms are not able to offer or accept. The shifted lines which do 

 occur, the "Raman lines," reveal the energy-values of the stationary 

 states of the scattering particles. 



We consider next the exceptions to the rule — the cases in which a 

 scattering particle may accept or surrender any quantity of energy 

 whatever within an appreciable continuous range, instead of merely 

 certain separate discrete amounts. This may be possible if the 

 energy conceded by the quantum is employed in altering the speed of 

 the particle, or in breaking the particle into pieces and imparting speed 

 to these — if it becomes kinetic energy of translatory motion of the 

 molecule or atom, or of the fragments thereof. Translatory motion is 

 non-quantized, which is a way of saying that it is not under the do- 

 minion of quantum-conditions which allow to it some values and deny 

 it others. Any amount of kinetic energy of translation is permitted 

 to a molecule or an atom, so far as we know. This suggests that any 

 amount of energy may be transferred when such a particle meets a 

 corpuscle of light, provided that so long as the energy is held by the 

 molecule or the atom it is held in this form. But there is another limi- 

 tation to be remembered — that imposed by Newton's principle of the 

 conservation of momentum. If a swiftly-moving corpuscle of rela- 

 tively small mass m strikes a slowly-moving body of much larger mass 

 AI, the latter cannot gain much speed in the encounter; for it cannot 

 acquire speed without acquiring momentum, and if it were to accept 

 for that purpose more than a very small fraction of the energy of m, it 

 would have to take more momentum than all that m possesses. 



Now relatively to an atom, a corpuscle of light is a body of very 

 small mass and very swift flight indeed; and a quantum of frequency 

 n cannot transfer to an atom of mass M, for use as kinetic energy of 

 translation, more than the fraction 2hnJMC'^ of its own initial energy — - 

 more than the quantity IWn^jMC^ altogether.^ For a quantum belong- 

 ing to the visible spectrum the fraction IhnjMC^ is of the order of 10~^ 

 even for an impact with the lightest of all atoms. The utmost possible 

 shift in frequency of the scattered light would bear only this proportion 

 to the primary frequency, and would be indistinguishable. But the 

 higher the frequency of the quantum, and the lower the mass of the 



^The formula is approximate, but the approximation is very close in all practical 

 cases. For the derivation of this and the accurate formula, see A. H. Compton, 

 Bull. Nat. Res. Council, 20 (1922) or my Introduction to Contemporary Physics, pp. 

 148-149. 



