Answer
$12.75~eV$ of energy must be supplied to the hydrogen atom.
Work Step by Step
We can find the difference in energy of the hydrogen atom in the ground state and in the state $n=4$:
$\Delta E = E_f - E_i$
$\Delta E = \frac{-E_0}{n^2} - (-E_0)$
$\Delta E = \frac{-13.6~eV}{4^2}-(-13.6~eV)$
$\Delta E = 12.75~eV$
$12.75~eV$ of energy must be supplied to the hydrogen atom.
