Is the Doppler effect for atomic spectra a purely realistic effect?

i am now studying the Doppler effect in a thermal atomic gas

If an atom travels in velocity v along x direction

at some time, it emits a photon in some direction

the momentum of the emitted photon can be well approximated with the free one

thus the momentum of the atom after the emission is well defined

We can then determine the energy of the photon with the energy conservation law

In this procedure, the Doppler effect apprarently depends on the MASS of the atom

However, the fomulae given in the book does not depends on the MASS but only on the velocity of the atom


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You might want to show an example where you calculate the Doppler shift according to your method. For example, let's say that a hydrogen atom is initially moving in the positive x direction at 0.1c, and it then makes a transition from an n=2 state to the ground state, emitting a photon in the positive x direction. What wavelength do you get for the photon (1) by your method, and (2) by the method given in your textbook?

It's true that the wavelength of the photon will depend, very slighly, on the mass of the atom. This is because the atom's final momentum is not the same as its initial momentum. The effect on the photon's wavelength is small, however.

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