Quantum Yield: Efficiency of Photochemistry

Quantum yield (Φ) measures the efficiency of a photochemical reaction: it is the number of molecules that react (or product molecules formed) divided by the number of photons absorbed. If 100 photons are absorbed and 75 molecules react, the quantum yield is 0.75. The Stark-Einstein law states that each molecule absorbs exactly one photon in the primary step, so the primary quantum yield can never exceed 1.

Quantum yield matters because it tells chemists how effectively light is converted into chemical change, which decides the economics of photopolymerisation, photography, and solar energy conversion. For JEE and NEET, it is the central numerical concept of photochemistry, linking the mole concept (through the einstein, one mole of photons) to reaction stoichiometry.

Key Concepts

The primary quantum yield counts only the immediate result of photon absorption and obeys Φ ≤ 1 by the Stark-Einstein law. The overall quantum yield counts final products and can be less than 1 when excited molecules lose energy through fluorescence or heat before reacting, or enormously greater than 1 in chain reactions, where one photon starts a chain that produces thousands of product molecules (the H2 + Cl2 reaction reaches Φ up to 106). An einstein is Avogadro's number of photons (one mole of photons), letting photochemists work in moles. Competing deactivation pathways (fluorescence, heat loss) waste absorbed energy and lower the yield.

Formulas

Φ = (moles of reactant consumed or product formed per second) / (einsteins of photons absorbed per second). Equivalently, Φ = (rate of the photochemical reaction)/(rate of photon absorption). Quantum yield is dimensionless. The formula assumes all absorbed photons are counted (scattered or transmitted light must be excluded) and that the measured product comes from the photochemical path alone.

Worked Example

A sample undergoing photolysis absorbs 0.0040 einstein of light and produces 0.0030 mol of product. The quantum yield is Φ = 0.0030/0.0040 = 0.75. This means 75% of absorbed photons successfully drive the reaction, while the remaining 25% are lost to fluorescence, internal conversion, or heat. Contrast this with the photochemical chain reaction H2 + Cl2 → 2HCl: absorbing just 1.0 × 10-6 einstein can produce 0.10 mol of HCl through chain propagation, giving Φ = 0.10/(1.0 × 10-6) = 1.0 × 105. The Stark-Einstein law still holds for the primary step (one photon, one Cl2 split); the huge overall yield comes from the chain, not from one photon doing many primary acts.

Common Misconceptions

• Quantum yield can never exceed 1. Only the primary yield is capped at 1. Overall yields in chain reactions routinely reach thousands or millions.
• Brighter light raises the quantum yield. Intensity raises the reaction rate, but quantum yield is a ratio of molecules per photon, which stays roughly constant as intensity changes.
• Every absorbed photon causes a reaction. Excited molecules often deactivate by emitting light or heat before reacting, which is why many photochemical yields sit well below 1.

Real-World Applications

Photographic film uses high-yield chain development of silver grains. Photopolymerisation for 3D printing and dental fillings depends on initiators with good quantum yields. Photosynthesis converts light to chemical energy with quantum yields around 0.1 per CO2 fixed. Solar cell engineers maximise the related quantum efficiency, electrons collected per photon, using the same thinking.

Quantum yield is simply molecules reacted per photon absorbed, capped at 1 for the primary step but free to soar in chain reactions. With the einstein as your photon mole and the ratio formula in hand, any photochemistry numerical becomes a straightforward division.