According to Bohr model of hydrogen atom, the electron orbits in circular orbits around the nucleus. when I'm asked to find the energy needed to ionize the hydrogen atom, I calculate the energy stored in the electron. this energy is consisted of kinetic energy and electric potential energy.
But, I was said that in order to get more precise results, I I have to calculate the "Reduced Mass" of the problem because the nucleus also orbits around the center of mass.
My question is why do we care about the velocity/movement of the nucleus in calculating the energy of the electron? solving the "reduced mass" problem gives my the energy of "the whole system" instead of the single electron. so why do we need to do that? is the energy of the electron changes somehow when the nucleus also orbits around the center of mass?