# Momentum of a relativistic atom

I have been solving a problem where you should derive the formula for doppler effect when a source of light is an atom moving at a relativistic velocity v. I understood everything in the solution except for why was the formula for impulse of the atom used as if it's not relativistic i.e. p=m*v? Is it maybe because the atom is so heavy that the lorentz factor wouldn't change the momentum noticeably?

• Someone made some error somewhere :) Maybe recoil effect was calculated in the atom frame, that's what I would do. Feb 5 '21 at 21:23

There is nothing wrong on writing the relativistic momentum as $$p = mv$$ as long as you are saying that $$m = \gamma m_0$$, where $$m_0$$ is the rest mass (inertial mass). In other words, the equation $$p = mv$$ is relativistic, the Lorentz factor is simply compacted onto the mass, meaning that the mass you are using to calculate isn't the rest mass but rather the relativistic mass.