Understanding the Relationship Between Energy and Frequency

[jd12345]

Why is energy proportional to frequency? Does this question have an answer or is it a fundamental thing that just happens?

 

[Fewmet]

Why is energy proportional to frequency? Does this question have an answer or is it a fundamental thing that just happens?

It is an experimental result. When you measure the maximum energy of ejected electrons in the photoelectric effect experiment and plot it against the frequency of the light that caused the emission (see example here), you get a straight line with a slope that is Planck's constant h. Applying the formula for a straight line and taking the binding energy of the electron into account, the equation of the line is E=h√.

 

[tiny-tim]

hi jd12345!

Why is energy proportional to frequency?

for light, it's a straightforward result from special relativity …

(i'll use unit with h = c = 1)

a photon moving in the x-direction with frequency e^α and energy E is a wave, with phase 2πe^α(t-x) and energy-momentum 4-vector (E,E,0,0)

a second observer moving in the x-direction with rapidity e^β will see the light red-shifted, with phase 2πe^α-β(t-x) and energy-momentum 4-vector (Ee^α-β,Ee^α-β,0,0)

so energy divided by frequency is a constant for that particular photon

(there's probably a similar proof for electrons etc … would anyone else like to have a go at that?)