Photochemical Reaction Rates

Introduction

Some reactions require light to create reactive excited states or radicals. Their rates can depend on wavelength and the number of photons absorbed, not merely on reactant concentration or temperature. Photochemical kinetics therefore adds a controllable energy input while still requiring careful attention to absorption, mechanism and competing pathways.

Core explanation

A photon has energy E=hν=hc/λ, so shorter-wavelength light has higher energy per photon. A molecule must absorb a suitable wavelength to enter a relevant excited state. Light passing through without absorption cannot directly initiate that molecule's photochemical event. The absorption spectrum and the light source together determine how many useful photons are taken up.

The incident light intensity is not identical to absorbed photon rate. Some light is reflected, scattered or transmitted. In a dilute solution obeying Beer–Lambert behavior, absorbance depends on concentration and path length, so changing either can change the absorbed fraction. A kinetic experiment should report or control the photon flux reaching the sample and its absorption, not just lamp wattage.

Quantum yield Φ can be defined as the number of specified molecular events divided by the number of photons absorbed. If one absorbed photon causes one direct chemical conversion, Φ may be near one in an idealized case. A value below one can reflect relaxation, fluorescence, recombination or competing processes. A value above one is possible in chain reactions where one photon initiates many propagation events. The definition requires specifying which event is counted.

For a direct one-photon process at low conversion, a simple rate may be proportional to absorbed photon flux if each absorption has a constant conversion probability. But increasing light intensity need not increase rate forever. Reactant depletion, saturation, recombination and transport can change the dependence. In radical photochemistry, steady-state radical concentration may scale with the square root of light intensity under certain termination mechanisms, producing a non-linear rate relation.

Wavelength matters beyond total power. Two lamps supplying equal energy per second at different wavelengths deliver different photon counts and may excite different molecules. A lower-energy wavelength may not be absorbed or may not access the required excited state. Conversely, a high-energy wavelength could produce unwanted side reactions. “More light” is therefore incomplete without spectral information.

Photochemical examples include atmospheric NO₂ photolysis and laboratory photoisomerization. For a simplified atmospheric initiation, NO₂ + hν → NO + O under appropriate wavelengths; subsequent oxygen chemistry can form ozone. The full atmospheric network is more complex, and the equation should be treated as one step rather than an overall ozone-production equation.

Temperature can still matter. Excited-state decay, radical reactions and diffusion often have temperature-dependent rate constants even when the initiating event is photon absorption. Photochemistry does not replace ordinary kinetics; it couples light input with thermal reaction steps.

Step-by-step reasoning

1. Identify the absorbing species and relevant wavelength range. 2. Distinguish incident from absorbed photon flux. 3. Define the molecular event used in quantum yield. 4. Relate absorption to initiation and subsequent mechanism steps. 5. Check for saturation, chains, temperature effects or side reactions.

Visual explanation

Draw a beam entering a solution cuvette. Split it into reflected, transmitted and absorbed arrows. An absorbed photon excites molecule A , which branches to product, fluorescence or relaxation. Put Φ as product events divided by absorbed photons, not incident photons.

Real-world analogy

Sending invitations does not equal attendance: some are lost, some recipients decline and one attendee may invite many others. Incident photons are invitations; absorbed photons are received, while quantum yield tracks the resulting specified events.

Real-world example

NO₂ photolysis in sunlight creates NO and reactive oxygen atoms under suitable wavelengths. That initiation participates in atmospheric ozone chemistry, showing why daylight can change rates even at similar gas concentrations.

Why?

Why can quantum yield exceed one? A single absorbed photon can initiate a chain in which reactive intermediates carry out multiple product-forming propagation steps before termination.

Common misconception

“Lamp power alone determines photochemical rate.” Only relevant absorbed photons initiate the intended process; wavelength, geometry, concentration and competing loss routes matter.

Worked example

A sample absorbs 2.0×10¹⁸ photons per second and forms 5.0×10¹⁷ specified product molecules per second. Quantum yield is Φ=(5.0×10¹⁷)/(2.0×10¹⁸)=0.25 product molecules per absorbed photon. This means one counted product forms for about four absorbed photons on average under those conditions; it does not imply every fourth photon follows a fixed deterministic sequence.

Quick check

1. Should quantum yield use incident or absorbed photons in its denominator? Answer: Absorbed photons for the stated definition.

Exam focus

Use E=hc/λ, distinguish incident and absorbed intensity, define the counted event in Φ and recognize that chain reactions can have Φ above one.

Advanced insight

Photochemical rate laws can require solving excited-state and radical steady-state balances. Their apparent light-intensity order may be one, one-half or another value depending on initiation and termination pathways.

Summary

Photochemical rates depend on suitable photon absorption and subsequent reaction pathways. Quantum yield counts specified events per absorbed photon, while light intensity and wavelength affect initiation. Chain and saturation effects can make rate dependence nonlinear.

Practice questions

1. Which photon has higher energy, 300 nm or 600 nm? Answer: The 300 nm photon because energy is inversely proportional to wavelength. 2. Why may a strong lamp fail to speed a reaction? Answer: Its light may not be absorbed at a useful wavelength, or another step may limit rate. 3. What does Φ=2 mean for a specified product? Answer: Two product events occur per absorbed photon on average, often possible through chain propagation.