含义Meaning
激发态分子以发光方式回到基态的比例。辐射与非辐射（内转换、系间窜越、猝灭）过程竞争。
The fraction of excited molecules that return to the ground state by emitting light, as radiative decay competes with internal conversion, intersystem crossing and quenching.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(k_r\) | 辐射速率常数radiative rate constant | s⁻¹ |
| \(k_{nr}\) | 非辐射速率常数之和sum of non-radiative rate constants | s⁻¹ |
| \(\tau_F\) | 荧光寿命fluorescence lifetime | s |
| \(F, A, n\) | 积分荧光强度、吸光度、折射率integrated emission, absorbance, refractive index |
推导Derivation
激发态衰减 \(d[S_1]/dt = -(k_r + k_{nr})[S_1]\)，指数衰减，寿命 \(\tau = 1/(k_r + k_{nr})\)。
S₁ decays exponentially with lifetime \(\tau = 1/(k_r + k_{nr})\).
发光的分数为分支比 \(k_r/(k_r + k_{nr})\)。
The emitting fraction is the branching ratio \(k_r/(k_r + k_{nr})\).
相对法：与已知标准（如硫酸奎宁 Φ = 0.55）在相同条件下比较积分荧光，并校正吸光度和溶剂折射率。
Relative method: compare with a standard (quinine sulfate Φ = 0.55), correcting for absorbance and refractive index.
适用条件与局限Assumptions & limitations
相对法要求低吸光度（A < 0.1）以避免内滤效应。
Keep A < 0.1 to avoid inner-filter effects.
寿命测量需时间分辨技术（TCSPC）；多指数衰减说明有多种发光物种或环境。
Lifetimes need time-resolved methods; multi-exponential decay signals heterogeneity.
例题Worked example
荧光素在 0.1 mol/L NaOH 中 Φ ≈ 0.93，τ ≈ 4 ns，所以 k_r ≈ 2.3×10⁸ s⁻¹。
Fluorescein in 0.1 M NaOH: Φ ≈ 0.93, τ ≈ 4 ns → k_r ≈ 2.3×10⁸ s⁻¹.