Quantum Yield
Definition, Formula & Experimental Determination
Photochemistry
Quantum Mechanics
Molecular Reactions
Photochemistry Fundamentals
φ
Quantum Yield
Measuring Photochemical Efficiency
What is Quantum Yield?
Quantum yield is the ratio of the number of molecules reacted or formed to the number of photons absorbed in a photochemical reaction.
Measures Reaction Efficiency
Indicates how effectively photons convert to molecular products
Denoted by φ (phi)
Fundamental parameter in photochemistry studies
Dimensionless Quantity
Ratio of molecular counts or molar quantities
φ =
Nmolecules / Nphotons
Mathematical Representation
Basic Formula
φ = Number of molecules reacted or formed� ──────────────────────� Number of photons absorbed
Molar Form (Einsteins)
φ = Moles of substance reacted or formed� ────────────────────────────� Moles of photons (Einsteins) absorbed
One Einstein = One mole of photons = 6.02 × 10²³ photons
Understanding Quantum Yield Values
φ = 1
Normal Quantum Yield
1 photon = 1 molecule
• Direct one-to-one reaction
• Each absorbed photon initiates one molecular event
• Ideal photochemical efficiency
φ > 1
High Quantum Yield
1 photon → many molecules
• Chain reaction mechanism
• One photon triggers multiple molecular reactions
• Efficient cascade process
φ < 1
Low Quantum Yield
Many photons → 1 molecule
• Energy loss mechanisms
• Multiple photons required per reaction
• Inefficient photochemical process
One Einstein = One mole of photons = 6.02 × 10²³ photons
How to Determine Quantum Yield
To determine quantum yield φ experimentally, two measurements are needed in the same amount of time
1
Moles of Substance
Number of moles reacted or formed
Measure product formation
Track reactant consumption
Chemical analysis methods
2
Moles of Photons
Einsteins absorbed by substance
Measure light energy absorbed
Use actinometer calibration
Calculate photon flux
Detailed Experimental Procedure
a
Molecules Reacted
Light Exposure
Shine light on chemical reactant for specific duration
Measurement
Determine amount of chemical reacted or product formed
Analysis Methods
Chemical analysis or spectroscopy techniques
Result: Moles of substance reacted or formed
b
Photons Absorbed
Energy of One Photon
E = hc / λ
h = Planck's constant
c = Speed of light
λ = Wavelength
Energy of One Einstein
E = Nhc / λ
N = Avogadro's number (6.02 × 10²³)
Fundamental Constants & Units
Planck's Constant (h)
6.626 × 10⁻²⁷ erg·s
6.626 × 10⁻³⁴ J·s
Velocity of Light (c)
3.0 × 10¹⁰ cm/s
3.0 × 10⁸ m/s
Wavelength (λ)
Units: cm, m, or Å (Angstrom)
1 Å = 10⁻⁸ cm = 10⁻¹⁰ m
Unit of φ
Dimensionless (no unit)
Ratio: molecules / molecules or moles / moles