What does the constant mean in this equation for the energy levels of an atom?

My textbook, Silberberg & Amateis, *Chemistry: The Molecular Nature of Matter and Change* (9th ed.), gives the following equation for calculating the energy level of an atom:
$$E = \pu{-2.18E-18 J}\left(\frac{Z^2}{n^2}\right)$$
Where $Z$ is the charge of the nucleus.


They never explained what the constant term that is multiplying the (Z/n)^2 term means, or where it comes from. Where does this come from? It looks similar to the [Rydberg equation](https://en.wikipedia.org/wiki/Rydberg_formula#:%7E:text=This%20formula%20of%20f%20%3D%20c,elements%20from%20aluminum%20to%20gold.), but I still can't see its relation to it exactly.




Essentially, the equation conveys how the energy of a one-electron atom varies with factors such as the nuclear charge and electronic orbit number.


$-2.18\times10^{-18}\ \mathrm J$ is an empirically obtained factor, but you can also derive it from first principles using Bohr's atomic model.


$$2.18\times10^{-18}\ \mathrm J=\frac{(k\_\mathrm ee^2)^2m\_\mathrm e}{2\hbar^2}$$


Where $k\_\mathrm e$ is Coulomb's constant, $e$ is the electronic charge, $m\_\mathrm e$ is the mass of an electron, and $\hbar$ is the reduced Planck constant.


You can find the derivation on Wikipedia: <https://en.wikipedia.org/wiki/Bohr_model>


Intuitively, you can think of $-2.18\times10^{-18}\ \mathrm J$ as the energy of a hydrogen atom system with an electron in its first orbit. Here $Z=1$ and $n=1$.


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