Read the following passage and answer the questions.
A glass discharge tube is filled with hydrogen gas at low pressure. A high voltage is applied across the tube, and an electric current passes through the gas. The tube then glows. A spectrometer is used to study the light that comes out of the tube. In Bohr’s model, the electron of a hydrogen atom can stay only in certain allowed energy states, called stationary states. The energy of the electron in the \(n\)th state is \(E_n=-13.6/n^{2}\ \mathrm{eV}\), where \(n = 1, 2, 3, \ldots\) In the tube, fast-moving electrons collide with the hydrogen atoms. These collisions raise some atoms to states of higher energy. Such an excited atom does not stay in that state for long. It soon falls back to a lower state and gives out a photon.
The energy levels of hydrogen are drawn as horizontal lines on an energy scale, using the formula given in the passage. As \(n\) increases, the levels
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → come closer and closer together and approach 0 eV
The size of \( E_n=-13.6/n^{2}\ \mathrm{eV} \) falls quickly as \( n \) grows. The first few levels and the gaps between them are:
\( E_1=-13.6\ \mathrm{eV} \)
\( E_2=-3.40\ \mathrm{eV} \)
\( E_3=-1.51\ \mathrm{eV} \)
\( E_4=-0.85\ \mathrm{eV} \)
\( E_2-E_1=10.2\ \mathrm{eV} \)
\( E_3-E_2=1.89\ \mathrm{eV} \)
\( E_4-E_3=0.66\ \mathrm{eV} \)
Option (1) stay equally spaced — Incorrect. The gaps of 10.2 eV, 1.89 eV and 0.66 eV are far from equal.
Option (2) move farther apart — Incorrect. Each gap is smaller than the one below it. So the levels get closer as \( n \) increases.
Option (3) crowd together near \(-13.6\ \mathrm{eV}\) — Incorrect. \( -13.6\ \mathrm{eV} \) is the ground state, the lowest level. The widest gap, 10.2 eV, lies just above it.
Option (4) come closer and closer together and approach 0 eV — Correct. For a very large \( n \), \( E_n \) becomes very small. So the levels bunch up just below 0 eV, the energy for \( n=\infty \).
NCERT (2026-27):
Energy levels – “… In this diagram, the highest energy state corresponds to n = ∞ … and has an energy of 0 eV. … Observe how the energies of the excited states come closer and closer together as n increases.”
