The minimum energy required to excite a Hydrogen atom from its ground state is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10.2 eV
In the Bohr model the energy of the hydrogen atom in level \( n \) is \( E_n = -13.6/n^{2}\,\mathrm{eV} \). The minimum excitation lifts the electron from the ground state \( n = 1 \) to the next level \( n = 2 \).
\( E_1 = -13.6\,\mathrm{eV} \)
\( E_2 = -13.6/4 = -3.4\,\mathrm{eV} \)
\( \Delta E = E_2 - E_1 = -3.4 - (-13.6) = 10.2\,\mathrm{eV} \)
Note: A similar question was also asked in CUET (UG) 2026 on 18-05-2026 (Slot 1), and in CUET (UG) 2025 on 20-05-2025 (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.”