physical chemistry - Calculating the ionization energy for hydrogen

What energy would be needed to remove the electron from the $n = 4$ level of the hydrogen atom?

• $\pu{−3.49 * 10^{−17} J}$


• $\pu{−1.36 * 10^{−19} J}$


• $\pu{+2.18 * 10^{−18} J}$


• $\pu{+1.36 * 10^{−19} J}$

I assume that the way to do this is to start from the Rydberg formula,

$$ E = \mathcal{R}Z^2 \left( \frac{1}{n_i^2}-\frac{1}{n_f^2} \right), $$

set the initial level of the electron as $n_i = 4$, and the final level corresponding to removing the electron (ionization) as $n_f = \infty \implies \frac{1}{\infty^2} = 0$, leading to

$$ E = \pu{13.6*\frac{1}{4^2} eV = 0.85 eV = 1.36*10^{-19} J}. $$