Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The highest energy state corresponds to the electron revolving in the orbit closest to the nucleus.
Reason (R): The energies of the excited states come closer and closer together as \( n \) decreases.
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A and R are both false.
Assertion (A) The highest energy state corresponds to the electron revolving in the orbit closest to the nucleus. — False. The orbit closest to the nucleus (n = 1) has the lowest energy, \( E_1=-13.6\,\mathrm{eV} \). This is the ground state. The energy rises in the outer orbits, and the highest energy state is \( n=\infty \), with an energy of 0 eV.
Reason (R) The energies of the excited states come closer and closer together as \( n \) decreases. — False. The levels come closer together as n increases. From \( E_n=-13.6\,\mathrm{eV}/n^2 \), the gap from n = 1 to n = 2 is 10.2 eV. The gap from n = 2 to n = 3 is only 1.89 eV. As n decreases, the gaps between the levels grow.
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.”
Energy Levels – “… In this diagram, the highest energy state corresponds to n = ∞ … and has an energy of 0 eV. This is the energy of the atom when the electron is completely removed (r = ∞) from the nucleus and is at rest. Observe how the energies of the excited states come closer and closer together as n increases.”