# Current flowing uphill

When the external voltage is reduced to zero, there is still a current; some electrons get across to the collector without help. Even when the polarity of the source is reversed some current remains. The energy of some of the liberated electrons is high enough to overcome the retarding potential and reach the collector. This is apparent from the left side of the graph, which shows the presence of remnants of current despite an adverse electric field. We have the equivalent of spring water flowing uphill against the force of gravity.

 -eV0 Emax = e Vo = hf - W slope = h lowest frequency = work function = W /t f ! 4 frequency -W ^ fo fl f2 f3

Figure 13.4 Experimental data giving the value of the cut-off potential as a function of the light frequency. The points lie on a straight line, exactly as predicted by Einstein's equation.

Figure 13.4 Experimental data giving the value of the cut-off potential as a function of the light frequency. The points lie on a straight line, exactly as predicted by Einstein's equation.

Eventually, when the adverse voltage reaches a certain value called the cut-off or stopping potential, even the most energetic electron is repelled, and the current stops. In Figure 13.3 the stopping potentials for photocurrents liberated by light of frequencies f1, f2 and f3 are V1, V2 and V3 respectively. The higher the frequency of the incoming light, the greater the cut-off potential; the exact relationship is plotted in Figure 13.4.

The most energetic photoelectron has an energy eV, just enough to overcome an adverse potential V. Figure 13.4 shows this energy as a function of the frequency of the light shining on the photosensitive surface. According to Einstein's equation it is equal to the energy of the photon minus the work function W, the energy used up by the electron in getting out of the metal.

All the experimental data on the photoelectric effect agree with the predictions of one simple equation! Abandoning his former scepticism Millikan conceded 'this is a bullet-like, not a wave-like effect'. As a bonus, the slope of the graph in Figure 13.4 provides an independent measurement of Planck's constant, h.

Note that momentum does not come into play, because the electron is basically attached to the lattice, which is much heavier, and absorbs all the momentum.