The intrinsic pathways of de-excitation of an excited molecule, M*, is the sum kM of the rate constants for these processes is equal to the reciprocal of the excited-state lifetime τ₀: \begin{equation} k_M = k_r + k_{ic} + k_{isc} = k_r + k_{nr} = 1/τ_0 \end{equation}

where kr is the rate constant for fluorescence emission and knr is the sum of first-order rate constants for nonradiative decay pathways, such as internal conversion, intersystem crossing, etc. When a fluorophore molecule reaches the lowest vibrational level of the excited electronic state, the energy quantum for the return to the ground state may be accepted by a suitable molecule present in the solution. This results in the loss of the fluorescence intensity. This process is called quenching. When there is a bimolecular interaction between the excited molecule and the quencher, it can be described as follows:

\begin{equation} M^* + Q → M + Q \end{equation} \begin{equation} rate_q = k_q [Q] [M* ] \end{equation} The product k_q[Q] is pseudo-first-order, where k_q, is the second-order rate constant for quenching process and [Q] is the quencher concentration. Therefore, the de-excitation pathways of the molecule M*, in the presence of quencher, Q, is given by \begin{equation} k_{M^'} = k_r + k_{nr} + k_q [Q]= 1/τ_0 + k_q [Q] \end{equation} The fluorescence quantum yield in the absence of quencher (φ0): \begin{equation} φ0 = k_r / (k_r + k{nr}) = k_r τ0 \end{equation} The quantum yield in the presence of quencher (providing dynamic quenching as the only quenching mechanism) is given by: \begin{equation} φ = k_r / (k_r + k{nr} + k_q [Q]) = k_r /(1/τ_0 + k_q [Q]) \end{equation} Dividing eq 5 by eq 6 and rearranging, one obtains \begin{equation} φ_0/ φ = 1 + k_q τ0 [Q] = 1 + K{SV} [Q] \end{equation}

where K_SV (=k_q τ₀) is the Stern-Volmer constant for the collision quenching process, τ₀ and τ are the fluorescence lifetimes in the absence and the presence of Q, and k_q is the bimolecular rate constant for the quenching process.

The measured steady-state fluorescence intensity is proportional to the number of emitted photons. Therefore, in general the fluorescence intensity and φ are proportional to each other. If F₀ and F are the steady-state fluorescence intensities in the absence and in the presence of quencher, respectively, then one write the Stern-Volmer eq as follows: \begin{equation} F_0/F = 1 + K_{SV} [Q] \end{equation}

This equation is used to calculate K_SV or k_q. A plot of F₀/F versus the quencher concentration, [Q], is linear (Stern-Volmer plot) with an intercept of 1 and a slope equal to the Stern-Volmer quenching constant, K_SV, if only dynamic quenching occurs. When the plot is found to be linear, the Stern-Volmer constant is calculated from the slope of the plot. Then, kq can be calculated if the excited-state lifetime in the absence of quencher (τ₀) is known. The rate constant of quenching, k_q, is equal to the quencher diffusion constant in the case of 100% efficient quenching, which lies typically in the range of 109-1010 M-1s-1. One can easily calculate the diffusion controlled rate constant, k_d, for the bimolecular process in a solvent by using the relation, k_d = 8RT/3000η, where R is the gas constant, T is the Kelvin temperature and η is the viscosity of the solvent. The value of k_q may exceed the diffusion-controlled range when static quenching also occurs in addition to the dynamic quenching.

In dynamic quenching, the fluorophore and quencher collide, inducing a loss of fluorophore energy. Then the fluorescence lifetime of these colliding fluorophore molecules is lower than that of the fluorophore molecules not participating in the dynamic process in solution. Therefore, the mean fluorescence lifetime measured in the presence of dynamic quenching will be lower than the mean lifetime measured in the absence of the quenching. In terms of life time, one can write the Stern-Volmer eq as follows: \begin{equation} τ_0/τ = 1 + k_q τ_0 [Q] \end{equation}

Time-resolved experiments in the absence and presence of quencher also allow one to calculate K_SV and kq. One can compare the value k_q with that of diffusion controlled rate constant, k_d . One should remember that it is important to include time-resolved measurements in the quenching analysis. In static quenching, molecules are quenched a priori and thus do not contribute photons to the lifetime measurement.