Spectra of one-electron atoms

You will find the energy levels and the spectral lines of any atom or ion that has one electron.

The idea. The level $n$ has energy $E_n = -\dfrac{13.6\,Z^2}{n^2}$ eV. A jump gives a photon with the difference of two levels, and $\lambda = \dfrac{1240}{E}$ nm. The limit of a series has $n_i \to \infty$.

Your tasks.

1. In level_energy, return the energy of the level $n$ for the charge $Z$, in eV.
2. In wavelength_nm, return the wavelength of the photon from the jump $n_i \to n_f$, in nm.
3. In series_limit_nm, return the wavelength at the limit of the series that ends on $n_f$, in nm.