The energy required to excite an electron in hydrogen atom to its first excited state is

10.2 eV

The correct answer is Option (3) → 10.2 eV

Energy of electron in the nth orbit is given by

$E_n = -13.6 \left(\frac{1}{n^2}\right)\ \text{eV}$

For ground state (n = 1): $E_1 = -13.6\ \text{eV}$

For first excited state (n = 2): $E_2 = -13.6 \left(\frac{1}{4}\right) = -3.4\ \text{eV}$

Energy required to excite from n=1 to n=2:

$\Delta E = E_2 - E_1 = (-3.4) - (-13.6) = 10.2\ \text{eV}$

∴ Energy required = 10.2 eV