UPSC Combined Geo-Scientist, Mains · 2025 · Mains Paper II
Q1(m). Discrete levels and the resonance condition
Question
‘Discrete energy levels’ and ‘condition of resonance’ are essential conditions for discontinuous line spectrum. Explain.
Answer in brief
A line appears only where hν = Ej − Ei. Discrete levels allow only certain ΔE, hence only certain separate lines.
Key points
- Discrete energy levels: a bound atom or molecule has only quantised energies E₁, E₂, … So only certain gaps ΔE exist.
- Resonance condition (Bohr frequency condition): a photon is absorbed or emitted only if hν = Ej − Ei.
- Both together ⇒ only certain frequencies appear ⇒ a discontinuous line spectrum.
- If the levels were continuous, every ν would satisfy resonance ⇒ a continuous spectrum, as beyond the series limit.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
Coversline spectrumBohr frequency conditionresonance conditionquantised energy levelsseries limit
All parts of Question 1
- 1(a) Why Z > 1 for H₂ and He at all pressures5 marks
- 1(b) Corresponding state of H₂S for N₂ at 25 °C and 1 atm5 marks
- 1(c) Band structure of n-type and p-type semiconductors5 marks
- 1(d) Symmetry elements of orthorhombic Mg₂SiO₄5 marks
- 1(e) Fall of G with temperature at constant pressure5 marks
- 1(f) Z > 1 and f > P for the gas P(Vm − b) = RT5 marks
- 1(g) Overall equation and the role of each species5 marks
- 1(h) log k against pH for specific H⁺ catalysis5 marks
- 1(i) KCl salt bridge for a silver–lead cell5 marks
- 1(j) Equilibrium constant from standard potentials5 marks
- 1(k) Conditions for an acceptable wave function5 marks
- 1(l) No solution with E = 0 for the particle in a box5 marks
- 1(m) Discrete levels and the resonance condition5 marks
- 1(n) Rotational activity of CO and CO₂5 marks
- 1(o) Measuring light intensity with a chemical actinometer5 marks
- 1(p) Why watch hands glow in the dark5 marks