# Bohr Model and Exciting Electrons

So I've got a relatively simple question; I'm not currently taking any courses in chemistry but while I was helping someone review a quiz I came across a question we couldn't figure out. According to the Bohr Model, is the energy required to excite an electron from the n=3 to n=4 orbit generally greater or less than the energy required to go from n=4 to n=5? Also, why is this so? I can't seem to find a clear answer anywhere online, as just about every result involves directly computing energy required to bump the electron up a few levels in very specific cases.

• Asking why is the wrong question. That's the way the universe is. Once you accept quantization of energy levels, that's the result you get back. – Zhe May 3 '17 at 15:14

## 1 Answer

The energy difference between the orbits gets smaller the higher "up" you go.

For the classical bohr model the energy of a given orbit $n$ can be approximated by:

$E_n=-\frac{Z^2R_E}{n^2}$

where $Z$ is the charge of the nucleus and $R_E$ is the Rydberg energy. Since there is a $n^2$ in the divider the difference $E_{n+1}-E_n$ gets smaller and smaller.

This is explained in more detail here.

As for why this is the case: here we have to look into quantum mechanics and I guess this is outside the scope here. But if you are interested look up explanations of a particle in a 1D box. The spacing of the energy levels there follows the same trend and you can find explanations there on why this is the case.