While investigating the emission spectra of the elements, Moseley discovered the following empirical formula, relating the energy $E$ of the $K_\alpha$ line of an element to its atomic number $Z$:
| $E=0.75hcR\left(Z-1\right)^2$ | (2) |
where $h$ is Planck's constant, $c$ is the speed of light and $R$ is the Rydberg constant. Though Moseley didn't know it at the time, this formula was later justified by the early quantum mechanical model of the atom due to Bohr where the energy of the electron level $n$ is given by
| $E_n = \dfrac{hcRZ^2}{n^2}$. | (3) |
| We see that Moseley's law is just the energy difference between the $n = 2$ and $n = 1$ states for an atom with atomic number $Z-1$. (The reason that the formula is for $Z-1$ and not $Z$ is a very subtle one. See the appendix at the end of this write-up for more information.) |