Why is the reason for validity of the formula for wavelength of characteristic X-rays?

The wavelength of Characteristic X-ray emissions is given by the expression

$$frac{1}{lambda}=R_text{H} (Z_{eff})^2 left(frac{1}{n^2}-frac{1}{m^2}right)$$

Where $R_text{H}$ stands for Rydberg’s constant and $n$ & $m$ denotes the primary Quantum numbers of the shells involved in transition.

But it seems like the above expression treats the whole atom as a slightly modified version of Bohr’s model. Though it considers the $Z_{eff}$ it still treats the whole shell to be degenerate. But as we know that in multi electron system, the shells have subshells and subshells have orbitals that orbitals of a subshell are degenerate and not the whole shell, how could the validity of this expression be reasoned out?