Question

How much energy is required to remove an electron in the n=2 state from a hydrogen atom?

Answer 1

The energy of ionization of hydrogen atom in the state $n$ is given by

$$E=\frac{13.6\:\rm eV}{n^2}$$

Hence

$$E=\frac{13.6\:\rm eV}{2^2}=3.4\:\rm eV$$