VKC Notes · Photochemistry · Civil Services P-I · IFoS P-I · Geo-Scientist P-II
10.1 Photochemistry: Quantum Yield, Jablonski Diagram and H₂–Halogen Reactions
★★★ 2021–2025: 40 parts, 320 marks (Civil Services 11 parts / 120 m · IFoS 8 / 81 m · Geo-Scientist 21 / 119 m). The H₂–Br₂ mechanism and the Jablonski diagram come almost every year.
Syllabus lines. Civil Services and IFoS: “Absorption of light; decay of excited state by different routes; photochemical reactions between hydrogen and halogens and their quantum yields”. Geo-Scientist: “Decay of excited states by radiative and non-radiative paths. Fluorescence and phosphorescence, Jablonski diagram. Laws of photochemistry: Grotthus-Draper law, Stark-Einstein law … quantum yield and its measurement …, actinometry. Photostationary state. Photosensitized reactions. Kinetics of HI decomposition, H₂-Br₂ reaction, dimerisation of anthracene”. Norrish reactions are in the organic photochemistry notes (12.1).
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CSE 2024 Q7(a) = asked there; tap to open the solved answerSN = line kept in the short notes
10.1.1 Absorption of light: the Beer–Lambert law ★★★
Draw it in 60 s: axes l and I/I0; a falling exponential from 1 (60 %, 36 %, 22 %); on the same axes a dashed straight line for A rising from the origin.
- Lambert: each thin layer absorbs the same fraction of the light reaching it, −dI/dx = kI. Beer: that fraction is proportional to concentration. Together −dI/I = k′c dx; integrate from I₀ to I over 0 to l CSE 2021 Q5(b) 10m.SN
(10.1.1)
- ε (molar absorption coefficient, L mol⁻¹ cm⁻¹) = k′/2.303. Holds for monochromatic light, dilute solutions, no association or reaction of the solute.SN
- Absorbance adds; transmittance multiplies. Dye 1 g/100 cc transmits 60 % in 1 cm (A = 0.222): 2 g/100 cc gives A = 0.444, T = 36 %, 64 % absorbed; 90 % absorbed needs A = 1, l = 4.5 cm CSE 2025 Q5(b) 5m.SN
- 10 % transmitted in 1 cm (A = 1): in 0.5 cm A = 0.5, T = 31.6 %, 68.4 % absorbed (not 45 %) CSE 2023 Q8(c) 10m. 50 % transmitted, c = 0.04 M, l = 2 cm: ε = 0.301/0.08 = 3.76 L mol⁻¹ cm⁻¹ CSE 2024 Q6(a)(ii) 5m.
10.1.2 Laws of photochemistry and the einstein ★★★
- Grotthuss–Draper law: only light that is absorbed can cause a photochemical change.SN
- Stark–Einstein law (photochemical equivalence): in the primary step each molecule that reacts absorbs one quantum; one mole of photons (one einstein) activates one mole of molecules IFoS 2021 Q5(b) 8m.SN
(10.1.2)
- 600 nm: 199.4 kJ mol⁻¹; 300 nm: 398.8 kJ mol⁻¹: ratio 1 : 2, E ∝ 1/λ Geo 2022 Q1(p) 5m. 2500 Å: 478.5 kJ = 4.785 × 10¹² erg = 1.144 × 10⁵ cal mol⁻¹; 4.96 eV per photon Geo 2021 Q1(p) 5m.SN
- Threshold: 1.5 eV → λmax = 1240/1.5 = 827 nm (near infrared), 144.7 kJ mol⁻¹; 2.0 eV → 620 nm IFoS 2023 Q6(b) 15m.
- 511 nm photon: 234 kJ mol⁻¹ > D(Br–Br) 190 but < D(H–H) 432 kJ mol⁻¹; besides, H₂ is colourless and does not absorb visible light (Grotthuss–Draper). H₂ would need λ < 277 nm Geo 2024 Q1(p) 5m.SN
10.1.3 Quantum yield and actinometry ★★★
(10.1.3)
- Stark–Einstein predicts Φ = 1 for the primary step. Φ < 1: deactivation (fluorescence, collisions), recombination in the solvent cage, reverse reaction. Φ > 1: secondary steps; Φ ≫ 1: a chain Geo 2023 Q1(o) 5m.SN
- Primary quantum yield φ: for the primary act only (≤ 1); the overall Φ includes secondary steps. 100 mW at 400 nm, 40 % transmitted, 50 min: 180 J absorbed = 6.01 × 10⁻⁴ einstein; 0.4 mmol decomposed: Φ = 0.665 IFoS 2024 Q1(c) 8m.SN
- Chemical actinometer: a reaction of known Φ measures the light: Iabs = n/(Φt). Uranyl oxalate: UO₂²⁺ sensitises H₂C₂O₄ → CO₂ + CO + H₂O, Φ ≈ 0.5–0.6 (5.19 × 10¹⁸ molecules per 10.59 × 10¹⁸ photons: Φ = 0.490); oxalic acid titrated with KMnO₄. Ferrioxalate: Φ ≈ 1.2; Fe²⁺ read with 1,10-phenanthroline Geo 2025 Q1(o) 5m Geo 2024 Q14(d) 5m.SN
Solved PYQ CSE 2021 Q7(c) 20m
2500 Å, 10 mL of 0.05 M oxalic acid with 0.01 M uranyl sulphate; after 80 J absorbed, oxalic acid is 0.04 M. Find Φ.
- Decomposed: 0.01 mol L⁻¹ × 0.010 L = 1.0 × 10⁻⁴ mol = 6.022 × 10¹⁹ molecules.
- One photon: hc/λ = 7.95 × 10⁻¹⁹ J; photons in 80 J = 1.006 × 10²⁰.
- Φ = 6.022 × 10¹⁹ / 1.006 × 10²⁰ = 0.60: the uranyl ion absorbs and sensitises the decomposition.SN
| Data | Answer | Asked |
|---|---|---|
| 1 J at 480 nm, H₂ + Cl₂, Φ = 10⁶ | 4.01 × 10⁻⁶ einstein → 4.0 mol Cl₂, 8.0 mol HCl | CSE 2024 Q6(a)(i) 10m |
| 1 cal at 2100 Å gives 1.44 × 10⁻⁵ g H₂ | 7.35 × 10⁻⁶ einstein; Φ(HI) = 1.95 ≈ 2 | Geo 2023 Q10(b) 5m |
| Propanal, 302 nm, 15 000 erg s⁻¹, Φ(CO) = 0.54 | 2.28 × 10¹⁵ photons s⁻¹ → 1.23 × 10¹⁵ CO s⁻¹ | Geo 2022 Q15(a) 10m |
| Dipropyl ketone, 313 nm, 50 W, Φ = 0.21 | 1.31 × 10⁻⁴ einstein s⁻¹ → 2.75 × 10⁻⁵ mol C₂H₄ s⁻¹ (0.099 mol per hour) | IFoS 2021 Q6(b) 15m |
10.1.4 Decay of excited states: the Jablonski diagram ★★★
Draw it in 60 s: three singlet lines (S0, S1, S2) on the left, T1 lower on the right; straight arrows for light (A up, B and C down), wavy or dashed ones for IC and ISC.
| Process | Type | Spin | Time |
|---|---|---|---|
| A Absorption S₀ → S₁, S₂ | radiative | allowed (ΔS = 0) | 10⁻¹⁵ s (vertical, Franck–Condon) |
| D Internal conversion S₂ → S₁ (with vibrational relaxation) | non-radiative | same multiplicity | 10⁻¹² s |
| B Fluorescence S₁ → S₀ | radiative | allowed | 10⁻⁹–10⁻⁷ s, stops at once |
| E Intersystem crossing S₁ → T₁ | non-radiative | forbidden (spin–orbit coupling) | 10⁻¹¹–10⁻⁶ s |
| C Phosphorescence T₁ → S₀ | radiative | forbidden | 10⁻³ s to minutes: afterglow |
- Label the diagram, radiative vs non-radiative, decay routes CSE 2022 Q5(b) 10m CSE 2023 Q5(b) 10m CSE 2024 Q5(a) 10m Geo 2023 Q1(p) 5m. Singlet vs triplet: paired spins, S = 0, multiplicity 1; parallel, S = 1, multiplicity 3. For the same configuration T₁ lies below S₁ (Hund, exchange) IFoS 2022 Q6(a) 10m.SN
- Emission is at lower frequency than absorption (Stokes shift): energy is lost by vibrational relaxation first; phosphorescence is lower still because T₁ < S₁ IFoS 2025 Q6(a)(ii) 5m. ISC to the long-lived T₁ is the usual route to photochemistry (diradical-like) CSE 2022 Q5(b).SN
- Glowing watch hands: a phosphor (ZnS:Cu, SrAl₂O₄:Eu,Dy) stores energy in triplet or trap states and emits slowly: phosphorescence Geo 2025 Q1(p) 5m. “Phosphorescence delayed, fluorescence spontaneous”: both are spontaneous emission; they differ in spin rule and lifetime, so the statement is half right Geo 2023 Q9(e) 2m.
- Resonance fluorescence: atoms (Hg 253.7 nm, Na D lines) have no vibrational levels, so they re-emit at the absorbed wavelength; justified at low pressure; collisions quench it Geo 2023 Q9(d) 2m.
- Raman vs luminescence: Raman is instant scattering (≈ 10⁻¹⁴ s) via a virtual state at ν₀ ± νm; luminescence needs real absorption Geo 2024 Q1(m) 5m.
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