QUESTION #99

# How is the photon energy related to photon frequency?

Asked by: Ed Vinzulis

The light emission is attributed to atomic transitions, where an electron 'jumps' from a higher atomic energy level to a lower one.

The frequency of the photon is given by the following relation:

f = (E2-E1)/h

Where f is the frequency of the photon, E2, E1 are the energy levels (E2>E1) and h is the Planck's constant (h=6.63*10^-34 J.s)
Answered by: Alex, Ph.D Physics

Let me tell you first 'what' a photon is then I'll give you the relationship between 'E' (energy) and 'f' (frequency) of a photon. If you want the answer really quick, just move to the bottom of this message.

In 1905, Einstein published 3 works on different areas (One about the 'Photoelectric Effect', other about the 'Brownian Motion' and the other was the famous 'Special Relativity' - actually these are not the true titles of his works, but it gives you a rough idea). In one of them, about the Photoelectric Effect, Einstein recovered the old idea that light was composed of 'tiny' particles, and this relationship emerged due to the failure of the classical wave description of light to explain some experimental results. The experiment was, in a condensed form, as follows:

Imagine a certain piece of metal that, when you put ultraviolet light on it, you can measure the energy of some electrons 'escaping' from the the metal. From the very basical wave mechanics, one would expect that if you increased the 'intensity' of the light you would see more energetic electrons pulling off from it (picture a little paper boat in a lake where you make some waves - the more 'intense' you make them, the more the boat will jump up with greater velocities). Well, actually experimental results tell you that this does NOT happens. When you increase the intensity of the wave, only the NUMBER of electrons emitted from the metal will increase - not its ENERGY. The observed result is that only when you increase the FREQUENCY of the light you are applying, then the energy of the electrons will be greater. That sounds really strange for the wave nature of light.

Looking at these results, Einstein proposed that light, 'when interacting with matter', interacts as a particle. Well, if it interacts like that, as a particle, you might think that it needs a certain mass. Not exactly. Using the Theory of Relativity, Einstein proposed that the particle of light, the so-called 'photon', had a ZERO 'rest mass'. It had only the relativistic mass (caused by its motion). Using as a 'glue' the work of Max Planck about the Black Body Radiation, Einstein suggested that the energy of the photon was related to the frequency of the wave by the equation:

E=hf,

where 'E' is the energy of the photon, 'h' is the so-called 'Planck's constant' and 'f' is the frequency.

You can read a real good history of this work in the Abraham Pais' 'Subtle is the Lord', it's the best biography of Einstein, I think.