If 13.6 eV of energy is required to ionise the hydrogen atom, then the energy required to remove an electron from the level n = 2 is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3.4 eV
In the Bohr model the energy of level n is \( E_n=-13.6\,\mathrm{eV}/n^2 \). The ionisation energy 13.6 eV is the energy needed to take the electron from \( E_1=-13.6\,\mathrm{eV} \) to \( E=0 \).
To remove the electron from level n = 2, it must in the same way be raised from \( E_2 \) to \( E=0 \).
\( \begin{aligned} E_2 &= -\frac{13.6}{2^2}\,\mathrm{eV} \\ &= -3.4\,\mathrm{eV} \end{aligned} \)
\( \begin{aligned} \text{Energy required} &= 0-E_2 \\ &= 0-(-3.4\,\mathrm{eV}) \\ &= 3.4\,\mathrm{eV} \end{aligned} \)
NCERT (2026-27):
Bohr Model of the Hydrogen Atom – “… Energy will thus be required to remove the electron from the hydrogen atom to a distance infinitely far away from its nucleus (or proton in hydrogen atom).”
Energy Levels – “… From Eq. (12.10), for n = 2; the energy E2 is –3.40 eV.”
\( \displaystyle E_n=-\frac{13.6\,\mathrm{eV}}{n^2} \qquad (12.10) \)