Bundle of energy, but does it have mass?

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myrhinobutt2
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This is a two part question. First question: what exactly is a photon? I know that it's essentially a bundle of energy, but does it have mass? Can it be related by E=mC^2?

Second question: If I were to find a perfectly smooth spherical mirror (also assuming the distance between atoms is sufficiently small that the light cannot escape) and somehow turn on a light inside, would the photons somehow build up and become jammed in there?
 
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Photons don't have mass but they have momentum. You don't write

E =mc^2 for a photon but you write E = h f , h being the Plank's constant and f being the frequency.

Photon, simply put, is the quantization of electromagnetic energy. Depending on the context, we could observe particle properties of photons (Compton scattering, photoelectric effect) or the more natural classical wave properties. People had been familiar more with the latter by the time it was discovered so photoelectric effect and Compton were quite a shock.