The energy of an electron in the nth orbit of a hydrogen atom is given by the expression $E_n = E_1 / n^2$, where $E_1$ is the ground state energy (-13.6 eV) . The 'ground state' corresponds to the principal quantum number $n=1$ . The 'first excited state' corresponds to the next higher energy level, which is $n=2$ .

Substituting $n=2$ into the energy formula: $E_2 = -13.6 / 2^2 eV$ $E_2 = -13.6 / 4 eV$ $E_2 = -3.4 eV$

Thus, the energy of the first excited state is -3.4 eV.