During the **formation of light**, the energy is converted to a particle (mass) using E=mc^{2}. But we know that photons do not have mass. What follows is a mathematical derivations

The particle has a momentum (p) defined by Planck’s constant (h) and wavelength ƛ as;

From relativity we know that;

From quantum mechanics energy is defined as;

*h* is the Planck’s constant

*f* is the frequency of oscillation of a particle.

Therefore;

Dividing all sides by C

From wave mechanics:

Substituting into the equation and doing the operation we get that;

but mass by speed (*MC*) is momentum (*p*) hence

From the wave mechanics equation above rearranging the equation gives us;

Substituting *p* with the first equation, we find that

The derivation of this equation shows that the photon formed has only velocity mass is zero because from

the value of *f* is zero because a photon is a wave packet that does not have a definite wavelength and therefore no frequency.

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I’m not great with math, but I think I was able to follow along with what you were doing. It’s nice to know that when physicists say photons don’t have mass, I don’t have to just take their word for it. The proof is there.

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