Choose the correct statements from the following:
A. The minimum energy required to free the electron from the ground state of the hydrogen atom is 13.6 J
B. The principal quantum number n labels the stationary states in the ascending order of energy
C. Bohr gave the basic idea of discrete energy levels
D. de Broglie hypothesis provided an explanation for Bohr's second postulate for the quantization of angular momentum of the orbiting electron
E. Line spectrum provides useful information about the atomic structure.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → B, C, D and E only
The statements are drawn from the Bohr model of the hydrogen atom.
(A) The minimum energy required to free the electron from the ground state of the hydrogen atom is 13.6 J — Incorrect. The ionisation energy of hydrogen is \( 13.6\,\mathrm{eV} \), which is only \( 13.6 \times 1.6\times10^{-19} = 2.18\times10^{-18}\,\mathrm{J} \). The unit is eV, not J.
(B) The principal quantum number n labels the stationary states in the ascending order of energy — Correct. \( E_n = -13.6/n^{2}\,\mathrm{eV} \), so the energy rises as \( n \) increases: \( n = 1 \) is the lowest state, then \( n = 2 \), and so on.
(C) Bohr gave the basic idea of discrete energy levels — Correct. Bohr postulated that the electron can stay only in certain stationary orbits with definite energies.
(D) de Broglie hypothesis provided an explanation for Bohr's second postulate for the quantization of angular momentum of the orbiting electron — Correct. If the electron wave forms a standing wave round the orbit, \( 2\pi r = n\lambda \) with \( \lambda = h/mv \), which gives \( mvr = nh/2\pi \), the quantisation of angular momentum.
(E) Line spectrum provides useful information about the atomic structure. — Correct. Each line corresponds to a jump between two energy levels, so the line spectrum reveals the energy levels of the atom.
NCERT (2026-27):
Energy Levels – “… 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. … The principal quantum number n labels the stationary states in the ascending order of energy.”
De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation – “… Thus de Broglie hypothesis provided an explanation for Bohr’s second postulate for the quantisation of angular momentum of the orbiting electron.”