# Determining the mass of a photon travelling at the speed of light

1. May 17, 2006

### Solidmozza

I'm just wondering about this when you are making calculations of photon mass. For instance, determining the mass of a photon travelling at the speed of light and having a frequency of 100 Hz. Which equation do you use, KE = 0.5mv^2 or do you use E=mc^2 (both in conjunction with the E=hf formula).

Thanks!

2. May 17, 2006

### Curious3141

A photon has no mass to speak of, because most of the time when we say mass, we mean "rest mass". The photon has zero rest mass.

What the photon does have is momentum. You can work out the momentum of the photon with De Broglie's equation $$p = \frac{h}{\lambda}$$.

Some people speak of "relativistic mass" which is the apparent mass gained because of motion. AFAIK, this concept has fallen out of favor, but if you want to compute the "relativistic mass" of a photon, you can do so by using $$E = pc = \frac{hc}{\lambda} = h\nu$$ together with $$E = mc^2$$ to determine m.

$$E_k = \frac{1}{2}mv^2$$ is a Newtonian approximation that only works for objects with rest mass at speeds of v<<c. It definitely does not work for photons or any object travelling close to the speed of light.

Last edited: May 17, 2006
3. May 17, 2006

### ImagineLab

First, photon has no mass.
Second, answer from those equations are only differ by 1/2. (Can you see that?)

4. May 17, 2006

### Andrew Mason

$KE=.5mv^2$ is the energy acquired by a body with rest mass being accelerated from 0 to non-relativistic speed v. Kinetic energy does not apply to a photon. A photon has no rest mass and always travels at c. Its energy, $E = h\nu = hc/\lambda = mc^2$. Photon momentum is $p = mc = h/\lambda$

AM

PS. Sorry about duplicating previous posts which, for some reason, I missed.

Last edited: May 17, 2006
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