Quantum Yield Simulator: Fluorescence Efficiency & Lifetime

simulator intermediate ~11 min
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Φ = 0.50 — 50% of absorbed photons re-emitted

With equal radiative and non-radiative rates (0.5 ns⁻¹ each), the quantum yield is 0.50 and the fluorescence lifetime is 1.0 ns. Half of absorbed photons produce fluorescence.

Formula

Φ = k_r / (k_r + k_nr) — quantum yield
τ = 1 / (k_r + k_nr) — fluorescence lifetime
E_stokes = hc(1/λ_ex - 1/λ_em) — Stokes shift energy

The Fate of an Absorbed Photon

When a molecule absorbs a photon, it enters an excited electronic state. From there, it has several options: emit a photon (fluorescence), convert the energy to heat (internal conversion), cross to a triplet state (intersystem crossing), or transfer energy to another molecule (quenching). The quantum yield measures what fraction of excited molecules choose the fluorescent pathway — a competition governed by the rates of each process.

Radiative vs. Non-Radiative Decay

The radiative rate (k_r) is an intrinsic property of the molecule, determined by the transition dipole moment between ground and excited states. The non-radiative rate (k_nr) depends on molecular flexibility, solvent interactions, and the availability of quenching pathways. Rigid, planar molecules like perylene and rhodamine have high k_r/k_nr ratios and bright fluorescence, while flexible molecules dissipate energy through bond rotations.

Fluorescence Lifetime

The fluorescence lifetime is the average time a molecule remains excited before emitting. Typical organic fluorophores have lifetimes of 1-10 ns. Lifetime is inversely proportional to the total decay rate: τ = 1/(k_r + k_nr). Because lifetime is sensitive to the local environment but independent of concentration, it is widely used in fluorescence lifetime imaging microscopy (FLIM) to map molecular environments inside living cells.

Applications in Science and Technology

Fluorescence is ubiquitous in modern science — from GFP-tagged proteins in cell biology to quantum dots in display technology, from forensic detection to environmental monitoring. High quantum yield materials are essential for bright, efficient fluorescence. This simulator lets you explore how radiative and non-radiative rates compete to determine fluorescence efficiency, and how the Stokes shift separates excitation from emission light.

FAQ

What is fluorescence quantum yield?

Fluorescence quantum yield (Φ) is the ratio of photons emitted to photons absorbed. A quantum yield of 1.0 means every absorbed photon produces a fluorescence photon; a yield of 0.01 means 99% of absorbed energy is lost to non-radiative processes like heat.

What determines quantum yield?

Quantum yield is determined by the competition between radiative (fluorescence) and non-radiative (internal conversion, intersystem crossing, quenching) decay rates: Φ = k_r/(k_r + k_nr). Rigid, planar molecules tend to have high quantum yields because they minimize vibrational energy loss.

What is the Stokes shift?

The Stokes shift is the wavelength difference between absorption and emission maxima. It arises because the excited molecule relaxes vibrationally before emitting, losing some energy to heat. Named after George Stokes who first observed it in 1852.

Why does fluorescence lifetime matter?

Fluorescence lifetime (τ) reveals the time a molecule spends in the excited state. It is sensitive to the local molecular environment — viscosity, pH, ion concentration — making it a powerful probe in fluorescence lifetime imaging microscopy (FLIM) for biological and materials research.

Sources

Embed

<iframe src="https://homo-deus.com/lab/photochemistry/quantum-yield/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub