5.3 Excited state lifetime and quantum yield

Excited state dynamics are crucial in photochemistry, determining how long molecules stay excited and how efficiently they use absorbed light. These factors influence everything from energy transfer to reaction rates.

Understanding excited state lifetimes and quantum yields helps predict and control photochemical processes. By measuring these properties, we can optimize reactions, design better sensors, and improve photocatalysts for various applications.

Excited State Dynamics

Excited state lifetime significance

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• Excited state lifetime measures time molecule spends in excited state before returning to ground state typically denoted as τ (tau) measured in seconds (nanoseconds or picoseconds)
• Determines time available for photochemical reactions influences energy transfer probability to other molecules affects competition between radiative and non-radiative decay processes
• Molecular structure solvent environment temperature and presence of quenchers (oxygen) impact excited state lifetime

Calculation of excited state lifetime

• Excited state lifetime formula $τ = 1 / (k_r + k_{nr})$ where $k_r$ is radiative decay rate constant and $k_{nr}$ is non-radiative decay rate constant
• Relaxation pathways include radiative decay (fluorescence phosphorescence) and non-radiative decay (internal conversion intersystem crossing)
• Longer lifetime corresponds to smaller decay rate constants shorter lifetime indicates faster decay processes
• Time-resolved spectroscopy techniques and fluorescence lifetime measurements experimentally determine excited state lifetime

Quantum yield concept

• Quantum yield measures efficiency of photophysical or photochemical process ratio of photons emitted to photons absorbed
• Formula $Φ = \frac{Number of events}{Number of photons absorbed}$ quantifies process efficiency
• Competition between radiative and non-radiative processes influences quantum yield higher values indicate more efficient radiative decay
• Molecular structure solvent effects temperature and presence of quenchers (triplet oxygen) or energy transfer acceptors (FRET pairs) affect quantum yield

Determination of quantum yield

• Chemical actinometry and comparative methods using standard fluorophores (rhodamine 6G) experimentally determine quantum yield
• Absorption spectra emission spectra and concentration of reactants and products required for calculation
• Quantum yield calculation steps:

1. Measure number of photons absorbed
2. Determine number of product molecules formed or reactant molecules consumed
3. Apply formula $Φ = \frac{moles of product formed}{moles of photons absorbed}$

• Ensure complete light absorption account for inner filter effects use appropriate excitation wavelength range for accurate measurements
• Quantum yield measurements evaluate photocatalyst efficiency (TiO2) optimize photochemical reactions (photopolymerization) design fluorescent probes and sensors (BODIPY dyes)