This term applies broadly to variations of quantum yields of photophysical processes (e.g. fluorescence or phosphorescence) or photochemical reactions (usually reaction quantum yields) with the concentration of a given reagent which may be a substrate or a quencher. In the simplest case, a plot of $\frac{{\mathit{\Phi }}^0}{\mathit{\Phi }}$ (or $\frac{M^0}{M}$ for emission) vs. concentration of quencher, $\text{[Q]}$, is linear obeying the equation: $$\frac{{\mathit{\Phi }}^0}{\mathit{\Phi }}\text{or}\frac{M^0}{M}=1+K_{\text{sv}}[\text{Q}]$$ In equation (1) $K_{\text{sv}}$ is referred to as the Stern–Volmer constant. Equation (1) applies when a quencher inhibits either a photochemical reactions or a photophysical process by a single reaction. ${\mathit{\Phi }}^0$ and $M^0$ are the quantum yields and emission intensity radiant exitance, respectively, in the absence of the quencher Q, while $\mathit{\Phi }$ and $M$ are the same quantities in the presence of the different concentrations of Q. In the case of dynamic quenching the constant $K_{\text{sv}}$ is the product of the true quenching constant $k_{\text{q}}$ and the excited state lifetime, ${\tau }^0$, in the absence of quencher. $k_{\text{q}}$ is the bimolecular reaction rate constant for the elementary reaction of the excited state with the particular quencher Q. Equation (1) can therefore be replaced by the expression (2): $$\frac{{\mathit{\Phi }}^0}{\mathit{\Phi }}\text{or}\frac{M^0}{M}=1+k_{\text{q}}{\tau }^0\left[\text{Q}\right]$$ When an excited state undergoes a bimolecular reaction with rate constant $k_{\text{r}}$ to form a product, a double-reciprocal relationship is observed according to the equation: $$\frac{1}{{\mathit{\Phi }}_{\text{p}}}=(1+\frac{1}{k_{\text{r}}{\tau }^0\text{[S]}})\frac{1}{A\cdot B}$$ where ${\mathit{\Phi }}_{\text{p}}$ is the quantum efficiency of product formation, $A$ the efficiency of forming the reactive excited state, $B$ the fraction of reactions of the excited state with substrate S which leads to product, and $\text{[S]}$ is the concentration of reactive ground-state substrate. The intercept/slope ratio gives $k_{\text{r}}{\tau }^0$. If $\text{[S]}=\text{[Q]}$, and if a photophysical process is monitored, plots of equations (2) and (3) should provide independent determinations of the product-forming rate constant $k_{\text{r}}$. When the lifetime of an excited state is observed as a function of the concentration of S or Q, a linear relationship should be observed according to the equation: $$\frac{{\tau }^0}{\tau }=1+k_{\text{q}}{\tau }^0[\text{Q}]$$ where ${\tau }^0$ is the lifetime of the excited state in the absence of the quencher Q.