Answer
It would require $3.4~eV$ of energy to ionize the atom.
Work Step by Step
We can find the energy when the hydrogen atom is initially in the n=2 state:
$E = \frac{E_0}{n^2}$
$E = \frac{-13.6~eV}{2^2}$
$E = -3.4~eV$
Therefore, it would require $3.4~eV$ of energy to ionize the atom.
