Originally Posted by

**AndresKiani**
So we have the Rydberg's Formula for 1 electron system such as Hydrogen or Helium Ion or any other one electron system.

*DeltaE = -2.18 x 10*^{18}(1/n_{final}^{2} - 1/n_{initial}^{2})

Though I came across, I new formula for the first time just now.

*DeltaE = (-Z*^{2}/n^{2})R ---> R = -2.18 x 10^{18 }J or 3.39 x 10^{15} Hz

So I'm guessing that the second equation can be used for both 1 electron and multi-electron systems? What is this formula called btw?

I'm rusty on the details of all this, but I rather think your second formula is Rydberg's formula for hydrogen-like atoms (i.e. ions with only one electron left). Have a look here:

Rydberg formula - Wikipedia, the free encyclopedia
Once you have more than one electron present, you get electron-electron repulsions and so the relationship of energy to nuclear charge becomes impossible to calculate exactly.