# Waves, Particles or Both….

Einstein won the Nobel Prize for this. If we shine some light of a high  enough frequency on a metal plate, electrons get ejected from the plate. We can attract them towards an anode and thus measure an electric current. The more electrons emitted per second, the larger the current.

OK so far. But, is the light shining on the plate a wave or a particle?

The details of the photoelectric effect come out differently depending on whether light consists of particles or waves. If it’s waves, the energy contained in one of those waves should depend only on its amplitude – that is, on the intensity of the light. Other factors, like the frequency, should make no difference. So, for example, red light and ultraviolet light of the same intensity should knock out the same number of electrons, and the maximum kinetic energy of both sets of electrons should also be the same. Decrease the intensity, and you should get fewer electrons, flying out more slowly; if the light is too faint, you shouldn’t get any electrons at all, no matter what frequency you’re using.

Does this happen? Actually, no, it doesn’t. If the frequency is too low, no electrons at all are emitted. If the intensity is decreased but the frequency is high enough, we just get fewer electrons and even if the light is very faint indeed, we still get some.

We have to backtrack a bit now. In 1900, Max Planck was working on the problem of how the radiation an object emits is related to its temperature. He came up with a formula that agreed very closely with experimental data, but the formula only made sense if he assumed that the energy of a vibrating molecule was quantised – that is, it could only take on certain values. The energy would have to be proportional to the frequency of vibration, and it seemed to come in little “chunks” of the frequency multiplied by a certain constant. This constant came to be known as Planck’s constant, or h, and it has the value 6.63 x 10-34 Js. EM radiation therefore can be thought of as ‘light-bullets’ – little chunks or photons which are frequency dependent. The energy of a photon therefore is E = hf or E = hc/λ

Planck actually didn’t realize how revolutionary his work was at the time; he thought he was just fudging the sums to come up with the “right answer,” and was convinced that someone else would come up with a better explanation for his formula. Einstein took him seriously.

If  the incoming photon energy  is more than the energy required by the metal to prise an electron loose from the electrostatic attraction of surrounding nuclei – the WORK FUNCTION ENERGY, different for different metals, the electron is hooked out and any remaining energy is taken up as kinetic energy of the emitted electron. So, it’s an all-or-nothing event. Too little and nothing happens. These energies are of the order of a few eV – useful when looking at the properties of new alloys for switching circuits on computers.

Einstein made the predictions in 1905 and eleven years later Robert A Millikan, also a Nobel laureate did the practical which agreed with it. Given that it all happened in the middle of the First World War, this was quite impressive.