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Photon mass question and theoretical experiment?

Ok, everyone says that photons have no mass, but i simply can't believe it. So I tried to do a mental experiment: Imagine that you have a perfect box (no electromagnetic losses) and you have an energy source in it. (a source with more capacity than you need) and an LED (3V, 1A). Considering that the box is perfect, the electrons from the source should transform into photons when it passes through the LED, and since there are no losses, the box should have constant mass.

I was thinking of this: (sorry, but it's more complicated than it should)

after how much time the source should have emitted 1 gram of electrons?

we have this

1A=6.2e18 electrons/s

1electron=9.1e-31kg=9.1e-28g

so 1 gram of electrons should have 1.09e27electrons in it

1s...6.2e18 electrons

x....1.9e27 electrons

therefore, x=3.06e8seconds, or somewhere close to 10 years (9.7 to be more exact).

now, assuming that the mass of the box is the same as it was 10 years ago, let's see how many photons have been converted from those electrons.

let's say that the wavelength of the light emitted is 589.3nm or 5.893e-7m

the energy of a single photon is hc/wavelenghth (where h is the planck constant) so E=3.37e-19J

the flux of electrons is 3W (1A x 3V) divided by the flux, or 8.9e18photons/secons

so in 10 years, there have been 2.8e27 photons emitted, which weigh 1 gram. Therefore, each photon weighs 3.56e-31kg. Is this correct?

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