Dipole–dipole energy transfer rate ∝ 1/r⁶ — a molecular ruler for nanoscale distances
FRET efficiency: E = 1/(1 + (r/R₀)⁶)
Förster radius: R₀⁶ = (9000·κ²·Q_D·J·ln10)/(128π⁵n⁴N_A)
Transfer rate: k_T = (1/τ_D)·(R₀/r)⁶
The (R₀/r)⁶ dependence makes FRET exquisitely sensitive to distances in the 1–10 nm range — the scale of protein domains, nucleic acid structures, and molecular machines. κ² = ⅔ for freely rotating dipoles (isotropic average).
Applications: protein folding, DNA hybridisation, live-cell imaging, single-molecule experiments.