Text: PHOTOELECTRIC EFFECT, STOPPING VOLTAGE The Photoelectric Effect, Stopping Voltage In an experimental arrangement similar to that of the cathode ray tube, scientists had observed another phenomenon. In contrast to the cathode ray tube, the cathode was not heated nor were large bias potentials used. Instead, it was found that when light impinged upon the surface of the cathode, electrons could be ejected from the cathode and picked up by the anode - a current could be measured. If an opposing bias voltage was established, a certain threshold potential was found above which no current would be measured. This was called the stopping voltage. It was determined that the stopping voltage was different when the cathode was made from different materials. But what was particularly troubling was the effect observed when the wavelength and intensity of the light which struck the surface were changed. The stopping potential did not change when the intensity of the light was changed. The current, however, did increase with increasing incident light intensity. The stopping potential increased when the wavelength of the incident light decreased. Furthermore, as the light intensity decreased, the current also dropped - nevertheless the onset of the current from the time the light first hit the surface was always instantaneous. This graph shows the typical results of an experiment. For a given light frequency and a particular metal for the cathode, the photocurrent is constant until a large enough retarding potential prevents the ejected electrons from reaching the anode. This potential is called the stopping potential and just matches the kinetic energy of the ejected electrons. When a higher energy light source is used (greater frequency, shorter wavelength), the ejected electrons possess a greater kinetic energy and so the stopping potential is correspondingly larger. This graph shows how the photocurrent increases when the light intensity increases but the wavelength is held constant. The stopping potential is the same however, suggesting that the kinetic energy of the ejected electrons is the same and hence independent of light intensity. This is the opposite of what would be expected classically. If light was of the classical wave-like nature, we would expect a time lag which would increase as the intensity of the light decreased. The total energy would be spread across a wavefront striking the entire cathode and nothing could happen until sufficient energy were absorbed. Also, why would the frequency of the light make a difference to the stopping potential? The amount of energy in a wave is carried by its amplitude. Here is a plot of the measured stopping potentials obtained for several light frequencies for two different metals. The slope of this plot is the same in both cases and is equal to Planck's constant h. The x-intercept corresponds to the lowest frequency light that is able to eject electrons for each metal. This frequency times Planck's constant is the work function of the metal, peculiar for each metal, and represents the amount of energy necessary for an electron to "climb" out of bulk metal materials. It was Einstein who, in 1905, took Planck's quantum hypothesis and applied it the photoelectric effect and showed how the consideration of the structure of matter has having quantized energy levels accounted precisely for these observations. This was a tremendous boost to the integrity of the quantum concept. In its interesting to note that it was this concept for which Einstein was awarded the Nobel Prize, and not for his work in relativity - something he developed the same year and for which he now is more well-known.

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