Engineering & Science
Stern-Volmer Fluorescence Quenching (I0/I) & Förster FRET Energy Transfer Efficiency
Calculate collisional fluorescence quenching intensity ratio I0/I = 1 + kq * tau0 * [Q] via the Stern-Volmer equation and nanoscale Förster resonance energy transfer efficiency E = 1 / (1 + (r / R0)^6).
Quantify dynamic collisional quenching and 1/r^6 spectroscopic rulers!
Dissolved oxygen, iodide, and acrylamide collisionally deactivate excited fluorophores during their natural unquenched lifetime tau0! The Stern-Volmer equation predicts a linear rise in unquenched-to-quenched fluorescence ratio: I0 / I = 1 + Ksv * [Q] = 1 + kq * tau0 * [Q], where kq is the bimolecular quenching rate constant (M^-1*s^-1), tau0 is lifetime without quencher (s), and [Q] is quencher molarity. At kq = 2.0e9 M^-1*s^-1, tau0 = 5.0e-9 s (Ksv = 10 M^-1), and [Q] = 0.15 M, fluorescence drops by I0/I = 1 + 10*0.15 = 2.5!
For donor-acceptor fluorophore pairs separated by distance r (1–10 nm), dipole-dipole Förster Resonance Energy Transfer (FRET) acts as a molecular ruler with sixth-power sensitivity around the Förster radius R0: E = 1 / (1 + (r / R0)^6)! At r = 4.5 nm with R0 = 5.4 nm, E = 0.7491 (74.91% transfer), whereas at r = R0 = 5.4 nm, efficiency is identically E = 0.50 (50%)!
| Spectroscopy Model | Parameters | Governing Equation | Calculated Result |
|---|---|---|---|
| Stern-Volmer Quenching | kq = 2e9, tau0 = 5 ns, [Q] = 0.15 M | I0/I = 1 + kq * tau0 * [Q] | I0/I = 2.5 (60% quenched) |
| FRET Molecular Ruler | r = 4.5 nm, R0 = 5.4 nm | E = 1 / (1 + (r/R0)^6) | E = 0.7491 (74.91%) |
| FRET at Förster Radius | r = 5.4 nm (= R0) | 1 / (1 + 1^6) | E = 0.50 (Exact 50% Midpoint) |
Stern-Volmer Fluorescence Intensity Ratio I0 / I
Computes 1 + kq * tau0 * [Q] after validating non-negative rate constant, lifetime, and quencher concentration.
=IF(OR(B2 < 0, B3 <= 0, B4 < 0), "Invalid Photophysics Inputs", ROUND(1 + (B2 * B3 * B4), 3))Förster Resonance Energy Transfer (FRET) Efficiency E
Evaluates E = 1 / (1 + (r / R0)^6) for donor-acceptor separation r (B5) and Förster distance R0 (B6).
=IF(OR(B5 <= 0, B6 <= 0), "Invalid Photophysics Inputs", ROUND(1 / (1 + ((B5 / B6) ^ 6)), 4))Try the example
Use the original values or change them to test your understanding.