How much energy ionises (a) a hydrogen atom whose electron is in the level n = 5, and (b) a He⁺ ion…

Hydrogen's levels: $E_n = -\dfrac{13.6\ \text{eV}}{n^2}$, and $-\dfrac{13.6\,Z^2}{n^2}\ \text{eV}$ for an ion with one electron. A jump gives a photon of energy $E_{\text{upper}} - E_{\text{lower}}$, with $\lambda = \dfrac{1240\ \text{eV nm}}{E}$. Lyman ends on $n = 1$, Balmer on $n = 2$, Paschen on $n = 3$.