Heat Capacity and the Photoelectric Effect

FIGURE 5.4 Light will only eject electrons from a metallic surface if the frequency is higher than a specific threshold, which varies for different metals. The maximum kinetic energy of the emitted electrons will increase if the frequency of the incident light increases. Einstein interpreted these observations as evidence for photons with energy E = hv. 

FIGURE 5.5 Schematic illustration of a photomultiplier tube. A single photon ejects an electron from the photocathode. The electron is accelerated by voltage differences, and knocks multiple electrons off each successive surface. The burst of electrons is collected at the end. 

A photon kicks an electron off the first surface the electron is accelerated by the voltage difference to the next electrode. The accelerated electron hits with sufficient force to knock off several more electrons, which in turn are accelerated to the next surface. After six or more of these stages, the cascade started by a single photon has become a burst of typically 106 electrons (total charge Q 106e = 1.6 x 10-13C). 

Another paper of Einstein s showed that quantization of energy also predicted that Dulong and Petit s heat capacity rule would only be valid at high temperatures. Assume that the only allowed energies are E = 0, hv, 2hv. nhv, where n can be arbitrarily large. The average energy is 

If we save only the largest terms in the numerator and denominator of Equation 5.11 (or use the exact expression, given in Problem 5-5) we find  

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