The energy required to remove an electron from the inner most orbit of the hydrogen atom to a distance far away from its nucleus is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 13.6\,\mathrm{eV} \)
The innermost orbit is \( n = 1 \), with energy \( E_1 = -13.6\,\mathrm{eV} \). A distance far away from the nucleus corresponds to \( n = \infty \), where the energy is zero. The energy required is the difference, which is the ionisation energy.
\( \displaystyle E_{\mathrm{required}} = E_\infty - E_1 = 0 - (-13.6\,\mathrm{eV}) = +13.6\,\mathrm{eV} \)
Why the other options are incorrect
Option (1) \( -13.6\,\mathrm{eV} \) — Incorrect. \( -13.6\,\mathrm{eV} \) is the energy of the electron in the ground state, not the energy that must be supplied to remove it.
Option (3) \( 3.4\,\mathrm{eV} \) — Incorrect. \( 3.4\,\mathrm{eV} \) is the energy needed to remove the electron from the first excited state \( n = 2 \).
Option (4) \( 0\,\mathrm{eV} \) — Incorrect. \( 0\,\mathrm{eV} \) is the energy of the free electron at rest far from the nucleus.
NCERT (2026-27):
Energy Levels – “… The lowest state of the atom, called the ground state, is that of the lowest energy, with the electron revolving in the orbit of smallest radius, the Bohr radius, a0. The energy of this state (n = 1), E1 is –13.6 eV. Therefore, the minimum energy required to free the electron from the ground state of the hydrogen atom is 13.6 eV. It is called the ionisation energy of the hydrogen atom.”