Collision frequency information

Collision frequency describes the rate of collisions between two atomic or molecular species in a given volume, per unit time. In an ideal gas, assuming that the species behave like hard spheres, the collision frequency between entities of species A and species B is:^[1]

Z=N_{\text{A}}N_{\text{B}}\sigma _{\text{AB}}{\sqrt {\frac {8k_{\text{B}}T}{\pi \mu _{\text{AB}}}}},

which has units of [volume][time]⁻¹.

Here,

$N_{\text{A}}$ is the number of A molecules in the gas,
$N_{\text{B}}$ is the number of B molecules in the gas,
$\sigma _{\text{AB}}$ is the collision cross section, the "effective area" seen by two colliding molecules, simplified to $\sigma _{\text{AB}}=\pi (r_{\text{A}}+r_{\text{B}})^{2}$ , where $r_{\text{A}}$ the radius of A and $r_{\text{B}}$ the radius of B.
$k_{\text{B}}$ is the Boltzmann constant,
$T$ is the temperature,
$\mu _{\text{AB}}$ is the reduced mass of the reactants A and B, $\mu _{\text{AB}}={\frac {{m_{\text{A}}}{m_{\text{B}}}}{{m_{\text{A}}}+{m_{\text{B}}}}}$