The visible spectrum of hydrogen

Hydrogen's levels are $E_n = -\dfrac{13.6\ \text{eV}}{n^2}$. You will make the program find the energy of the levels $n = 1$ to $6$, the upper level of the red line ($1.89\ \text{eV}$, landing on $n = 2$), and the shortest wavelength of the whole Balmer series, its limit. Then it draws the Balmer lines as a spectrum.

The idea. A jump down gives a photon of $E_{\text{upper}} - E_{\text{lower}}$, and $\lambda = \dfrac{1240\ \text{eV nm}}{E}$. The Balmer series limit is the jump from very far out, $E = 0$, down to $n = 2$.

Your tasks.

1. Inside the loop, work out E, the energy of the level n, in eV.
2. Find n_red, the upper level whose jump to $n = 2$ gives $1.89\ \text{eV}$.
3. Find lam_limit, the wavelength of the Balmer series limit, in nm.