Is Moseley's law related to the Bohr model? Moseley's rule states
$$\frac{hc}{\lambda} = (Z-\sigma)^2 R (\frac{1}{n^2}-\frac{1}{m^2})$$ 
In what way is this linked to/derived from the shell model (which I assume means the Bohr model)? My textbook says they are related.
 A: First, consider an atom consisting of one electron orbiting a nucleus with atomic number $Z$.  Since this is a hydrogenic atom, the energy levels of this electron are equal to 
$$
E = \frac{Z^2 R}{n^2}
$$
for $n = 1, 2, 3, ...$, where $R$ is the Rydberg energy.  If the electron goes from level $n$ to level $m$, it will emit a photon of energy
$$
E_\text{photon} = \Delta E_\text{electron} = Z^2 R \left( \frac{1}{n^2} - \frac{1}{m^2} \right).
$$
Hopefully you can see that this equation is very similar to the one you have above.  But why is $Z$ replaced with $(Z - \sigma)$ in your equation?  This is where the shell model comes in.  The idea is that the other electrons in filled lower shells (which are negatively charged) partially screen the charge of the nucleus.  In other words, to the outer electrons, it "looks like" there's a nucleus with a charge $(Z - \sigma)e$ at the center, rather than the "bare" nuclear charge $+Ze$.  We can therefore justify replacing $Z$ with $(Z - \sigma)$ in the above expression.
This isn't a rigorous proof by any standard, of course, but hopefully it shows the connection to the shell model.
