Photon Energy and Momentum

Light comes in packets called photons, and each photon carries a fixed amount of energy set entirely by its frequency: E = hf, where h is Planck's constant. A dim beam of blue light and a blazing beam of blue light are made of photons with the same energy each — the bright beam just has more of them. That is why turning up the brightness of red light never burns you: each red photon is too weak to break the chemical bonds in your skin, no matter how many you pile on. Ultraviolet light burns because each UV photon individually carries enough energy to damage molecules. More photons means more total energy delivered, but it is frequency alone that decides whether any single photon can do the damage.

Photons have zero mass, but they still carry momentum, p = E/c. This follows from relativity, not from the ordinary p = mv you use for objects with mass. A photon's energy is tied up entirely in its motion at speed c, and that energy translates directly into momentum. This matters later when photons bounce off electrons and transfer momentum to them, which is how collisions involving light conserve momentum just like collisions between particles.

This idea sets up the rest of the unit: once you accept light carries energy and momentum in discrete chunks, you can explain why electrons escape metal surfaces only above certain frequencies, and why photons striking atoms kick electrons up fixed energy rungs rather than any amount at all.