# 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. – stuffu Feb 5 at 21:23

## 1 Answer

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.

• You might want to point out that most physicists no longer use the concept of relativistic mass as pointed out by many other answers for example: relativistic mass and graivty. – M. Enns Feb 5 at 13:31
• @M.Enns I know. But that's not the case for most undergrad books (I'm here assuming that the asker is an undergrad) – Pedro Pinho Feb 5 at 13:34
• Thank you, everyone, it turns out that the author actually used relativistic mass which we didn't use before for the reasons you already mentioned and I didn't even think of using it. – Luka Milivojevic Feb 6 at 14:59