• id: JTHERM-02-N13
• title: Collision Frequency and Collision Rate
• tags: collision-frequency, mean-free-time, rate

The collision frequency $Z$ (number of collisions per molecule per unit time) relates to mean free path and mean speed: $Z = v_{\text{avg}}/\lambda = \sqrt{2}\pi d^2 n v_{\text{avg}}$. The mean free time (average time between collisions): $\tau = \lambda/v_{\text{avg}} = 1/Z$. At STP for nitrogen: $v_{\text{avg}} \approx 475$ m/s, $\lambda \approx 60$ nm, giving $Z \approx 7.9 \times 10^9$ collisions per second — each molecule collides nearly 8 billion times per second. The total collision rate per unit volume is $Z_{\text{total}} = \frac{1}{2}nZ$ (factor $\frac{1}{2}$ avoids double-counting).