When I was through with my exciting lecture one of them looked up from the display, and asked me what it's good for. Well, to show that the energy of the light is proportion to the frequency, I explained pa-ti-ent-ly. Ah, he said, but isn't the frequency of light the same as the energy?
See, that's what happens if ħ is equal to one in textbooks from the school level on. But more seriously, I figured the students had just learned from the very beginning on that frequency is essentially the same as energy. So then what's the big deal with the photoelectric effect? And why on earth did somebody get a Nobel Prize for it?
Well, until the last century students didn't have cellphones, h didn't have a bar, and light was a wave. A wave has an amplitude and a frequency. If you turn up the volume of your stereo its the amplitude of the sound waves that you change, not the frequency. If you turn the dimmer of your living room light, it's the light's amplitude that you change, not the frequency*.
In 1899 Thomson established that ultraviolet light caused electrons to be emitted from a metal surface. This was believed to be due to the atoms being shaken around by the infalling light waves, such that an electron could escape. In this case however, a higher light intensity should result in more emitted electrons and with more intensity the electrons should have a larger (average) kinetic energy.
So it came as a surprise what von Lenard found in 1902 when he studied how the energy of the emitted electrons varied with the intensity of the light. For this, he placed a negatively charged plate, the collector, opposite to the plate on which the light fell. The electrons that were emitted were repelled by the plate, and could only reach it if they had sufficiently high kinetic energy. If they reached the plate, they would cause a current that was measured.
Lenard found that there was a minimum voltage Vstop at the collector at which no electrons would reach it. The expectation was that increasing the light's intensity would then equip the electrons with more kinetic energy, and thus raise the repelling voltage necessary to stop them from reaching the collector. But it turned out Vstop did not depend on the intensity of the light. Instead it varied with the light's frequency.
In 1905 Einstein explained these findings by suggesting that the light should be thought of as quanta of frequency hf, with f the frequency that kick out the electrons from the plate. The electron would then carry the light quanta's energy, minus some constant energy that needs to be provided to get the electron off the metal surface. If the voltage is adjusted such that it stops the electrons from reaching the collector, e Vstop should be linear in the light's frequency with the constant of proportionality being Planck's constant. The plot below shows this dependence. On the y-axis you see the stopping voltage; the x-axis shows the frequency of the infalling light. The box in the corner is the computation of the curve's slope which gives Planck's constant.
Source: Robert A. Millikan's Nobel Lecture The Electron and the Light-Quant from the Experimental Point of View, The Nobel Foundation, 1923.
A. Einstein received the Nobel Prize in 1921 for "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect", and R.A. Millikan received the Nobel Prize two years later "for his work on the elementary charge of electricity and on the photoelectric effect".
And now you can set ħ = 1 again.
* Roughly speaking. I guess the spectrum of the emitted frequencies depends somewhat on the voltage.
This post is part of our 2007 advent calendar A Plottl A Day.