Read the following statements regarding energy levels, and identify the correct statements.
(A) The energy of an atom is least when its electron is revolving in an orbit closest to the nucleus
(B) the energy levels of the excited states come closer and closer together as principal quantum number increases
(C) ionisation energy of the hydrogen atom is the minimum energy required to free the electron from the ground state of the hydrogen atom
(D) as the excitation of hydrogen atom increases, the value of minimum energy required to free the electron from the excited atom decreases.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (C) and (D)
In the Bohr model of the hydrogen atom the energy of the level with principal quantum number \( n \) is
\( \displaystyle E_n = -\frac{13.6}{n^{2}}\,\mathrm{eV} \)
(A) The energy of an atom is least when its electron is revolving in an orbit closest to the nucleus — Correct. The orbit closest to the nucleus is \( n = 1 \), where \( E_1 = -13.6\,\mathrm{eV} \) is the most negative value, the ground state.
(B) the energy levels of the excited states come closer and closer together as principal quantum number increases — Correct. Because \( E_n \propto -1/n^{2} \), the gaps shrink as \( n \) increases:
\( E_2 - E_1 = 10.2\,\mathrm{eV} \)
\( E_3 - E_2 = 1.89\,\mathrm{eV} \)
\( E_4 - E_3 = 0.66\,\mathrm{eV} \)
(C) ionisation energy of the hydrogen atom is the minimum energy required to free the electron from the ground state of the hydrogen atom — Correct. This is the definition of the ionisation energy; for hydrogen it is \( 0 - (-13.6\,\mathrm{eV}) = 13.6\,\mathrm{eV} \).
(D) as the excitation of hydrogen atom increases, the value of minimum energy required to free the electron from the excited atom decreases. — Correct. The energy needed to free the electron from level \( n \) is \( 13.6/n^{2}\,\mathrm{eV} \), which falls as \( n \) rises:
\( n = 2:\ 3.4\,\mathrm{eV} \)
\( n = 3:\ 1.51\,\mathrm{eV} \)
NCERT (2026-27):
Energy Levels – “The energy of an atom is the least (largest negative value) when its electron is revolving in an orbit closest to the nucleus i.e., the one for which n = 1.”
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.”
Energy Levels – “… Observe how the energies of the excited states come closer and closer together as n increases.”