Thread: photon zero mass and e=mc^2

ok so i was wondering about photons having zero mass.
if e=mc^2 then c^2=e/m and e/c^2=m
if mass is zero you find yourself dividing by zero which is impossible
1/1 times the reciprocal of zero (lets say zero is 0/1) 1/1*1/0=1/0 as you can see its a paradox (as all of you already knew)
so how can zero mass have energy. well that's what i asked so i used a scientific calculator and e/c^2=m to try to calculate what the mass would be if e=mc^2 were true using the energy in joules(4*10^-19) of a photon and the speed of light (2.99792458*10^8) and got this
(i used the parentheses to make it less hard to see)

(4*10^-19)/(2.99792458*10^8)^2=0

ZERO
how could that be that would mean 0*c^2=4*10^-19
IMPOSSIBLE
i am no physicists i am just a freshman in high school but i don't see how this could be possible and know i must have made an error could someone please just show me where its driving me crazy.

The reason is that the famous E=mc² equation is actually a slightly simplified version. The full equation is
E²=(mc²)²+(pc)²
where p is momentum.

The photon has momentum but no mass and so the equation still works: E = pc

(You may have learnt that momentum = mass x velocity, but that is a classical mechanics calculation. In the case of quantum mechanics, it is better to think of the momentum of a photon as just an "intrinsic" value it has related to its energy).