UPSC Combined Geo-Scientist, Mains · 2023 · Mains Paper II
Q1(o). Stark–Einstein law and the quantum yield
Question
Consequence of which law of photochemistry predicts that a quantum yield for a photochemical process is one? Discuss the conditions under which the quantum yield (ϕ) of the reaction is (i) less than one; (ii) extremely large.
Answer in brief
Stark–Einstein law of photochemical equivalence (second law of photochemistry). ϕ < 1 when excited molecules lose energy or fragments recombine; ϕ ≫ 1 when the primary step starts a chain.
Key points
- Stark–Einstein law: each molecule taking part in the primary process absorbs one quantum ⇒ ϕ = 1; deviations come from secondary steps.
- ϕ < 1: excited molecules are deactivated before reacting, fragments recombine in the solvent cage, or the reverse reaction occurs.
- Examples of ϕ < 1: H₂ + Br₂ → 2HBr near room temperature, ϕ ≈ 0.01; 2NH₃ → N₂ + 3H₂, ϕ ≈ 0.25.
- ϕ ≫ 1: the primary step starts a chain, e.g. H₂ + Cl₂, ϕ = 10⁴ to 10⁶.
- A secondary step without a chain gives a small whole number: ϕ = 2 for 2HI → H₂ + I₂.
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.
CoversStark–Einstein lawquantum yieldphotochemical equivalencechain reactionH2–Cl2 reaction
All parts of Question 1
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- 1(g) Activation energy of 2HI → H₂ + I₂5 marks
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- 1(i) E° of Na⁺/Na from ΔrH° and ΔrS°5 marks
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- 1(m) Zero-point energy in joule and in cm⁻¹5 marks
- 1(n) Microwave activity of SF₆, CO, H₂, H₂O and CO₂5 marks
- 1(o) Stark–Einstein law and the quantum yield5 marks
- 1(p) Decay routes of a photoexcited molecule5 marks