What happens when the mass of nucleus is not infinite as compared to that of electron?(related to centre of mass)please explain in detail.

In all the formulas derived for energy ,radius, angular momentum,  from Bohrs model we assumed nucleus as having infinite mass compared to electron and therefore assuming that the nucleus is a fixed point around which the electron revolves.But actually both the nucleus and electron orbit around their centre of mass which lies very close to the centre of nucleus but not at the exact centre of nucleus, which we assumed in the derivations.

So all the calculations based on the formulas give error .

This can be corrected by replacing  mass of electron by the reduced mass of electron in the derived expressions.