Photoelectric Effect

What more can I say? Look at the diagram at the bottom!

But the history of this process is fascinating, and because I am the 'creator', you get to read it! Besides I think understanding the history makes it easier to remember and a much better story.

In the winter of 1900, Max Planck found a solution to the problem of energy & frequency distribution with heating. Classical physics couldn't explain nature. Planck worked on the problem and in so doing ushered in the quantum era by making a bizarre assumption that emission and absorption of energy can occur only in discrete amounts. So Max Planck introduced the 'quantum' concept to radiation. And this explanation did resolved the Planck's radiation problem. Because the idea seemed a bit loopy (well actually a lot loopy!) it did not attract much attention. The idea solved a specific problem using a strange thought process, and MOST IMPORTANTLY nobody had practically found independent evidence for the existence of the quantum.

Albert Einstein's contribution to this discussion was a theoretical explanation of a certain phenomenon, which showed that light was a stream of particles (which would later be named photons). The paper in question was titled, in German, Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt (for those who speak English, "On a Heuristic Viewpoint Concerning the Production and Transformation of Light"). Strangely, Planck did not agree with this explanation.

The phenomenon was not first seen by Albert Einstein, but his explanation is one of his two major contributions to the basic science underpinning radiotherapy. The other, of course, is $E = mc^2$!

The original observers included Henri Becquerel (1839), Willoughby Smith (1873), Heinrich Hertz (1887), J.J.Thomson (1899), Nikola Tesla (1901), and Phillipp Van Lenard (1902). Quite illustrious company, and surprising that no-one else twigged earlier. But then genius sees the solution when others can't even see the problem!

What Albert knew was that if you shine ultraviolet (UV) light onto a block of sodium metal, you would find that:


1. electrons could be ejected from metal surface if conditions were right
2. electrons were not ejected until the light frequency was higher than a specific value (i.e., only light of a certain 'colour', or MORE ultraviolet could cause the ejection)
3. electrons were not ejected below this frequency no matter how intense the light (i.e., it doesn't matter how many photons are thrown at the metal)
4. once above the frequency threshold, electron ejection was proportional to light intensity.
5. once above the frequency threshold, electron speed was proportional to the frequency excess over the threshold value (although predicted, this was only experimentally determined to be linear in 1915 by Robert Andrews Millikan)

With all the wisdom of the 'retrospectoscope', I also suspect that if you correlated the energy of the threshold UV light (using Planck's constant, $E = h\nu$) with the binding energy of electrons in sodium, they will be equal! But I don't know this for sure.

So, what did all of this show? I believe that this was one of the seminal (that means 'original' and 'ground breaking', not the other stuff!) proofs demonstrating the quantum nature of nature. The explanation runs something like this - the electron doesn't escape of its own accord because it has a 'binding energy' within the atom. Obviously if you put in enough energy to overcome the binding energy (think of it by saying "the releasing energy must exceed the binding energy before the electron can leave" - this is also applicable in relationships and getting out of the house on Saturday nights!) the electron will leave. The binding energy is a reflection of the internal state of the electron. You need to know that around the turn of the century, the physics of the electron was largely unknown.

really guys, this is a fascinating and huge area that makes for an exceptional case study of scientific thought, experimentation and theory development …. but not for here!

Rutherford's experiment delivered the insight that the POSITIVE charges and most of the MASS of the atom was in a 'nucleus', which sort of left out the electrons because they were small and NOT in the nucleus. Only later did the 'orbital' nature of the electron become apparent (thanks to Niels Bohr) , and it slowly developed that these orbits were tightly controlled. Anyway, this experimental data demonstrated that the energy of the photon will not cause the release of the electron until it exceeds the binding energy of the electron. The total energy is not relevant (that's why lots of low energy photons have no effect), the packet size has to be adequate first. Once the packet size is adequate, more photons means more electrons.

Anyway he provided this explanation in 1905. Simple really! So simple in fact that he was awarded the 1921 Nobel Prize for Physics for his explanation of the photoelectric effect.

Einstein even proposed an equation to describe the phenomenon (typical physicist!):

$E_{(photon)} = E_{(remove the electron)} + E_{(moving electron)}$

note that $E_{(photon)}$ is also $h\nu$ (that is Planck's Constant x Frequency), and $E_{(remove the electron)}$ is called the "Work function" (specifically the "work done needing to be done to remove the electron") which because of the relationship with the experimental data was defined as $h\nu_{0}$, which is the minimal energy needed for a photon to be able to eject one electron. The last term $E_{(moving electron)}$ is the kinetic energy (${1\over 2}mv^2$) of the electron, so when one photon ejects an electron, its speed is determined by the excess energy left after the work function is expended (i.e., $h\nu - h\nu_{0}$).

What Einstein did not delineate was the production of characteristic radiation. The reason is probably because the energy of xrays is much higher than UV light, and characteristic radiation only occurs after the ejection of a lower shell electron which are very tightly bound. But of course the production of characteristic radiation is even more proof for the quantum nature of matter!

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