Energy of a Photon:
A photon’s energy depends on its frequency, not its speed. Higher frequency means higher energy, like gamma rays versus radio waves.
Let p be the photon’s momentum; a measure of how much motion it has. For any photon, \[ p = {E \over c} \] So higher energy means greater momentum, even though its speed stays the same.
When we say "E = h · f", this is not kinetic energy. It’s the total quantum energy carried by the photon. Photons don’t have rest mass, so their energy isn’t split into rest mass plus kinetic. Instead, their energy is all electromagnetic in nature, essentially "p · c".
The photon’s momentum is measured via "p · c". Photons have energy "E = p · c", which comes from relativistic energy momentum relations. It’s how a photon can carry momentum even though its rest mass is zero.
The photon total energy is E which equals "h · f" and E also equals "p · c" such that "h · f = p · c", thus
This represents the fundamental relationship between light's wave-particle duality and its constant speed in a vacuum. It demonstrates that for a photon, its speed is always the ratio of its quantum energy to its momentum.
NB: 𝒉 above refers to Planck's constant = 6.626 × 10-34 J⋅s - see related post in this blog.
