An Experimental Investigation of de Broglie's Equation

The validity of de Broglie's equation is checked experimentally for electrons of 24 to 64 electron-kilovolts energy. The experiment consists essentially of deflecting a beam of cathode rays by an electrostatic field and, keeping the deflection constant, determining the relation between the intensity of the deflecting field, V, and the de Broglie wave-length, λ, of the deflected electrons. On the assumption that the motion of the electrons is in accordance with the laws of relativistic mechanics, and that the de Broglie wave-length is inversely proportional to the momentum, it is shown theoretically that the expression λ²V(1+h²/m₀²c²λ²)^1/2 should be independent of λ. Within the limits of experimental error this expression is found to be independent of λ, thereby demonstrating that the de Broglie equation, λ=h/mv, combined with the relativity expression for m, is adequate to describe the facts.