Question

Prove that photons are massless

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Answer 1

PROOF :

Let the energy be E

Let mass be m

Let the momentum be p

And finally speed of light is c

Einstein's mass , energy and momentum states that :

E² = m²c⁴ + p²c²

==> m²c⁴ = E² - p²c²

Divide both sides by c⁴ to get :

==> m² = E² / c⁴ - p² / c²

When object is at rest , the momentum is 0 :

Put p as 0 :

==> m² = E² / c⁴ - 0 / c²

==> m² = E² / c⁴ - 0

==> m² = E² / c⁴

Now , the rest energy of a photon is zero since its never at rest !

So put E as 0 :

==> m² = 0 / c⁴

==> m² = 0

==> m = 0 [ P.R.O.V.E.D ]

Hence the mass is zero !

Hope it helps :-)

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