If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from $n = 2$ is

3.4 eV

$\text{Energy required to make a transition from energy state n to m is }$

$\Delta E = -13.6 z^2(\frac{1}{n^2} - \frac{1}{m^2}) $

$\text{Energy required to remove an electron from n=2 is }$

$\Delta E = -13.6 1^2(\frac{1}{2^2} - \frac{1}{\infty^2}) = 3.4 eV$