Daily answer writing · Mon, 26 Oct, 2026
Quantum yield: why H₂ + Cl₂ has φ ≈ 10⁶ but H₂ + Br₂ only about 0.01
Define quantum yield and state the Stark–Einstein law of photochemical equivalence. The photochemical combination of $\ce{H2}$ and $\ce{Cl2}$ has a quantum yield of about $10^4$–$10^6$, whereas that of $\ce{H2}$ and $\ce{Br2}$ is only about 0.01 at room temperature. Explain this difference with the help of the reaction mechanisms.
Syllabus: Common to CSE Paper I, IFoS Paper I and Geo-Scientist Mains (physical): photochemistry, laws of photochemistry, quantum yield, photochemical chain reactions.
Model answer
Definitions
Stark–Einstein law: in the primary step each molecule that reacts absorbs one quantum ($h\nu$) of radiation; one einstein is absorbed per mole in the primary process.
$$\phi = \frac{\text{number of molecules reacted (or formed)}}{\text{number of photons absorbed}}$$
$\phi > 1$ means secondary (chain) reactions follow the primary step; $\phi < 1$ means the excited species are lost by recombination or deactivation.
H2 + Cl2: long chain, φ ≈ 104–106
Initiation: $\ce{Cl2 + h\nu -> 2Cl^.}$
Propagation:
$\ce{Cl^. + H2 -> HCl + H^.}$ $\Delta H \approx 436 - 431 = +5\ \text{kJ mol}^{-1}$, $E_a \approx 25\ \text{kJ mol}^{-1}$
$\ce{H^. + Cl2 -> HCl + Cl^.}$ $\Delta H \approx 242 - 431 = -189\ \text{kJ mol}^{-1}$
Termination: $\ce{2Cl^. ->[wall/M] Cl2}$
Both propagation steps are fast at room temperature, so one photon starts a chain of about $10^5$ cycles before termination: $\phi$ is very large (the mixture explodes in sunlight).
H2 + Br2: chain hardly runs, φ ≈ 0.01
Initiation: $\ce{Br2 + h\nu -> 2Br^.}$
The first propagation step, $\ce{Br^. + H2 -> HBr + H^.}$, is strongly endothermic: $\Delta H \approx 436 - 366 = +70\ \text{kJ mol}^{-1}$ ($E_a \approx 74$ kJ mol−1). At 298 K very few Br atoms cross this barrier; most recombine, $\ce{2Br^. -> Br2}$, before they react. HBr formed is also removed by $\ce{H^. + HBr -> H2 + Br^.}$ (inhibition). So far fewer than one HBr forms per photon. On heating, the slow step speeds up and $\phi$ rises.
Conclusion. The quantum yield depends on whether the chain-carrying atom can react faster than it recombines: Cl· can (nearly thermoneutral step), Br· cannot (+70 kJ mol−1 step).
Where the marks are
- Stark–Einstein law and definition of φ with meaning of φ above and below 1 (2 marks).
- H2–Cl2 mechanism: initiation, both propagation steps, termination (2 marks); why the chain is long, with the energetics (1 mark).
- H2–Br2 mechanism with the endothermic Br + H2 step identified (2 marks); recombination and HBr inhibition explaining φ ≪ 1, rise with temperature (2 marks).
- One-line conclusion linking φ to the slow step (1 mark).