# Energy of Hydrogen Atom (Electron vs Proton)

In many textbooks, energy changes of the hydrogen atom are attributed to the electron transitioning between energy levels. However, the energy itself is that of the whole system (proton+electron) so how can we attribute its changes to the electron? what's preventing us from attributing these changes to the proton??

• I don't know what text book you are using but when we solve the Schrodinger equation for hydrogen atom we solve for the whole atom as a two body problem. Apr 23, 2021 at 17:49

The energy is indeed that of the whole system, but the electron has a much smaller mass (1/1836) than the proton, so the latter does not contribute much here. But for accurate results you have to consider the proton as well. When you solve the corresponding two-body problem for two masses $$m_1$$ and $$m_2$$, you can reduce it to a one-body problem by using the reduced mass
$$\mu=\frac{m_1 m_2}{m_1+m_2}$$
If $$m_2$$ is much larger than $$m_1$$ then this equals approximately $$m_1$$, so $$m_2$$ doesn't contribute much to the energy and momentum of the whole system.