Q4(a)(i). Stark–Einstein law; quantum yield and why it is often low

The law of photochemical equivalence

1. Statement (Stark–Einstein): in the primary process of a photochemical reaction each molecule that reacts absorbs one quantum of radiation, hν, and is thereby activated: A + hν → A*
2. For one mole of molecules the energy absorbed is one einstein: E=N_Ahν=(N_Ahc)/(λ). For λ=400 nm: E=299.1 kJ mol⁻¹; at 254 nm, 471.0 kJ mol⁻¹, enough to break most single bonds.
3. The law applies to the primary step only. What the activated molecule does next (secondary, dark reactions) decides how many molecules finally react per photon.

Quantum yield

1. φ=(number of molecules reacted (or formed))/(number of photons absorbed)=(moles reacted)/(einsteins absorbed)
2. φ=1 when every activated molecule gives one product. φ>1 when secondary steps multiply the effect: HI photolysis, HI + hν → H + I, H + HI → H₂ + I, gives φ=2; the H₂ + Cl₂ chain gives very large φ. φ<1 when activated molecules are lost.

Causes of low quantum yield

1. Deactivation by collision (quenching): the excited molecule hands its energy to a neighbour as heat before it can react.
2. Radiative loss: the excited molecule re-emits the energy as fluorescence or, after intersystem crossing, phosphorescence.
3. Internal conversion: the electronic energy is degraded to vibrational energy within the molecule itself.
4. Recombination of fragments: in solution the radicals formed are held together by the surrounding solvent (cage effect) and recombine before they can escape and react.
5. Reverse reaction: the primary products react back (thermally or photochemically) to the starting material.
6. Insufficient energy or wasted light: the quantum absorbed excites the molecule but is too small to break the bond; light absorbed by products or impurities (inner filter) does not count towards reaction.

Application. the primary step of photosynthesis, charge separation in the reaction centre, has a quantum yield close to 1, because each later step is far faster than fluorescence or quenching; chemical actinometers (potassium ferrioxalate) use a reaction of known φ to count photons.