This equation is an analogy to the 3D Maxwell-Boltzmann distribution function of thermodynamic velocities of ideal gas molecules in space. Thus at time Δt and for a small target molecule with a diameter much smaller than the average distances of the molecules in the solution, the collision surface can be approximated to be a small target ball sitting in the center of the reference frame and assuming the molecules in the surroundings diffuse to it (Fig. ). We can divide the bulk volume into spherical shells with radius s and thickness dr. Integrating all shells in the bulk yield the hitting probability of the probes to the target. Using a relativity argument when 2𝐷 𝑟 ∆𝑡 of interest is much larger than the hitting area for a diluted solution, the probability of all bulk molecules within a spherical shell diffusing to the fixed target ball is the same as putting all molecules in the position of the target ball and diffusing to an imaginary target ball on the shell (Fig. ). Before the correction on the fractal nature of diffusion, this approximation yields number of collisions between this A and random Bs in Δt, derived from the historical integrations of Gaussian functions by Laplace, Jacobi, and Ramanujan and others with details described in the supporting information: