Energy of the electron in $n^{\text {th }}$ orbit of hydrogen atom is given by $E_n=-\frac{13.6}{n^2}$ eV. The amount of energy needed to transfer electron from first orbit to third orbit is

12.09 eV

For n = 1, $E_1=-\frac{13.6}{(1)^2}$ = -13.6 eV

and for n = 3, $E_3=-\frac{13.6}{(3)^2}$ = -1.51 eV

So required energy is

$E_3-E_1=-1.51-(-13.6)$ = 12.09 eV