Multi-electron systems [ENDORSED]

[Jiayi_Cao_3E]

Hello!

For the equation En = -hR/(n^2). I saw there was a modified version of this equation in the E-book - En = -(Z^2)hR/(n^2 ) for multi-electron atoms where Z is the atomic number of the atom. I understand that as Z increases, the energy of the electron decreases (gets more negative) since there are an increasing number of protons and nuclear attraction. However, I don't quite understand why it is Z squared instead of just plain Z. Anything helps!

[Chem_Mod]

The energy dependence is non-linear with respect to the nuclear charge.

Good question. Not something I discuss in class.