# Photon Momentum

Ed Aboud
Sorry if this is a ridiculous queation, but how does a photon have momentum if it hass no mass?

Crosson
They do it with energy! The equation for energy in relativity is:

$$E^2 = m^2 c^4 + p^2 c^2$$

Where m is the mass, p is the momentum, and c is the speed of light. Put in $m = 0$ and you get E = p c, so any massless particle with energy E will have momentum p = E/c.

Last edited:
dst
From the relativistic mass equation - e^2 = (pc)^2 + (mc^2)^2. Since it has no rest mass, the latter term disappears but we still have e^2 = p^2 * c^2.

Ed Aboud
Ah I see, thanks very much!

glueball8
what is the relationship between P and E?

Usaf Moji
They do it with energy! The equation for energy in relativity is:

$$E^2 = m^2 c^4 + p^2 c^2$$

Where m is the mass, p is the momentum, and c is the speed of light. Put in $m = 0$ and you get E = p c, so any massless particle with energy E will have momentum p = E/c.

Another way of getting the same result is to use the more popular form

$$E = mc^2$$

and solve for m (which can be regarded as the "relativistic mass"). Then just multiply by the velocity, which is c, and treat it like any other problem. You'll see that you get the same result, p = E/c.

Homework Helper
Gold Member
2022 Award
what is the relationship between P and E?

See post #2, if you mean P is the momentum?

lightarrow
Another way of getting the same result is to use the more popular form

$$E = mc^2$$

and solve for m (which can be regarded as the "relativistic mass"). Then just multiply by the velocity, which is c, and treat it like any other problem. You'll see that you get the same result, p = E/c.

...just by chance because the derivation is wrong. Photons are massless. The correct derivation is the one already written in post 2.