Photon momentum = p = mc?

Question

p=plank constant/wave length

plank constant = energy/frequency
wave length = c/frequency

p = energy/frequency/ c/frequency

p=energy/c

but energy=mc^2

so,
p = mc^2/c

p = mc.

According to this,

h/wavelength=mc

mass of a photon= hc/wavelength

IS THIS RIGHT ??????????

Answer 1

You are right, except for a minor error. Consider your last but one step and then your last step.......

You write, h/wavelength = mc
So then, m = h/wavelength.c
Not, m= hc/wavelength as you have written.

Yes, the formula m = h / wavelength . c is correct. Or alternately wavelength = h/mc .....a very well known form !!
However, 'm' is not mass of a photon but mass equivalent of the energy contained in the photon.

It might interest you to know that even matter particles exhibit dual nature (i.e. act as both a wave and as a particle under different conditions) and the formula for wavelength of matter waves is .......Wavelength = h/mv
where 'v' is the velocity of the matter particle. As you can see this formula is of the same form as Wavelength = h/mc for photon shown above.

However the formula for matter waves cant be derived directly from the formula for photon we are considering. There is a more elobrate derivation.

The important thing is you almost got it right..except for the last step. And there is no need to consider a seperate kinetic energy of the photon factor to be considered as some people have been asserting. The formula E = hf is going to take care of that since f= c/ wavelength.

Yes, Mass equivalent of energy of a photon is = h/wavelength. c
But remember, 'm' is not mass of a photon, but only the equivalent mass for the energy contained in the photon.
And this is a very well known formula. The formula
Wavelength = h/mc is also used to describe Compton effect.

P.S.- Please understand that issues such as rest mass or mass -variation and Energy-momentum formula being mentioned by some of the people posting here is really not relevant to the issue being discussed here. We are only talking about the energy of a photon (which has no mass) and the mass equivalent of that energy.

Answer 2

The full equation for the energy of a particle is E^2=m^2c^4 +p^2 c^2. For a photon, m=0, so E=pc. You went wrong when you wrote E=mc^2, which only takes into account the rest mass/energy of a particle.

Answer 3

You need to use the kinetic energy of the photon which is not E=mc^2. That is the equation used when converting matter to energy as one does in a fusion process. The links below should be able to explain where you went wrong better than I could.

Answer 4

Nope. You went wrong when you equated the energy of a photon with the energy from E = mc^2 - those are different energies. E = mc2 is the energy you could get if you had a certain amount of matter and converted it into pure energy, or if you had energy and converted it into matter. You are not converting your photon into matter, so you can't use that equation.

Answer 5

calculate for mass of a photon= hc/wavelength

u get

mass of a photon= some thing * 10 ^ -19

the mass of electron is 9.10938188 × 10^-31 kilograms

if the formula is right, photon is much heavier than electron. but that's not true

Answer 6

I thought photons were massless, which is why they can travel the speed of light. So the mass and momentum of a photon would be zero?

(very much a layman's answer, I realize.)