The energy required by an electron in hydrogen atom to jump from its ground state to its first excited state is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10.2 eV
In Bohr’s model the energy of the nth level of hydrogen is \( -13.6/n^{2} \) eV. The ground state is n = 1 and the first excited state is n = 2; the energy required is the difference.
\( \displaystyle E_n = -\frac{13.6}{n^{2}}\,\mathrm{eV} \)
\( \displaystyle E_1 = -13.6\,\mathrm{eV}, \quad E_2 = -\frac{13.6}{4}\,\mathrm{eV} = -3.4\,\mathrm{eV} \)
\( \displaystyle \Delta E = E_2 - E_1 = -3.4\,\mathrm{eV} - (-13.6\,\mathrm{eV}) = 10.2\,\mathrm{eV} \)
Note: A similar question was also asked in CUET (UG) 2025 on 20-05-2025 (Slot 2), 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.”