The energy required to excite an electron in hydrogen atom to its first excited state is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10.2 eV
The energy levels of hydrogen in the Bohr model are \( E_n = -13.6/n^{2}\,\mathrm{eV} \). The ground state is \( n = 1 \) and the first excited state is \( n = 2 \).
\( \displaystyle E_1 = -13.6\,\mathrm{eV} \)
\( \displaystyle E_2 = -\frac{13.6}{4} = -3.4\,\mathrm{eV} \)
\( \displaystyle \Delta E = E_2 - E_1 = -3.4 - (-13.6) = 10.2\,\mathrm{eV} \)
Note: A similar question was also asked in CUET (UG) 2026 on 18-05-2026 (Slot 1), and in CUET (UG) 2023 on 30-05-2023 (Slot 2).
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 – “… 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.”