So Today I was taught about the Moseley's law and its relation with Bohr's formula :
$$\frac{hc}{\lambda} = R \left(\frac{(Z-\sigma)^2}{n^2}-\frac{(Z-\sigma)^2}{m^2}\right)$$
My understanding is that in $(Z-\sigma)$, Z is the number of protons and $\sigma$ is related to (but not exactly) the number of electrons that is in lower shells.
So my question is that if the electron jumps to a lower level, how could value of $\sigma$ not change as stated in the Moseley's formula?
For example, let's say that an electron in L shell is knocked out. Then one electron jumps from M shell to L shell to fill the hole, the electrons under the jumping electron will change from 9 to 2. Therefore, the value of $\sigma$ should at least change and not remain constant, right?
However my professor taught me that in the example that I just mentioned, the value of $\sigma$ would remain as 9 (theoretically). How is that possible?