The energy of a Hydrogen atom in its first excited state is

The correct answer is Option (1) → \( -3.4\,\mathrm{eV} \)

In the Bohr model the energy of the hydrogen atom in the level \( n \) is

    \( \displaystyle E_n = -\frac{13.6}{n^{2}}\,\mathrm{eV} \)

The ground state is \( n = 1 \), so the first excited state is \( n = 2 \).

    \( \displaystyle E_2 = -\frac{13.6}{2^{2}}\,\mathrm{eV} = -3.4\,\mathrm{eV} \)

Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.

NCERT (2026-27):
Energy Levels – “… The atom is then said to be in an excited state. From Eq. (12.10), for n = 2; the energy E₂ is –3.40 eV. It means that the energy required to excite an electron in hydrogen atom to its first excited state, is an energy equal to E₂ – E₁ = –3.40 eV – (–13.6) eV = 10.2 eV.”