Question

How do you calculate the momentum of a photon?

Answer 1

The momentum of a photon is given by `E/c hat n` where `hat n` is the unit vector in the direction in which the photon is moving, `E` is its energy, and `c` is the speed of light.

Explanation:

For any particle of mass `m` (this is the so called invariant mass of the particle, often called the rest mass and denoted by `m_0`), the energy and the momentum are related by

`E^2-|vec p|^2c^2 = m^2c^4`

For the photon, the mass `m` is zero and this leads to

`|vec p| = E/c`

Note that the formula
`vec p = {m vec v}/sqrt{1-v^2/c^2}`
which is valid for massive particles, fails for the photon since both `m` and `1-v^2/c^2` vanish for it.