Collision Frequency and Mean Collision Time
In the dilute hard-sphere model, z = v_avg/lambda and tau = lambda/v_avg; scaling must account for speed, number density, and collision diameter.
Why this shows up in the exam
Collision-rate comparisons · Finding mean collision time · Wall-hit and molecular-collision estimates
Learn the idea
Collision frequency equals molecular speed divided by mean free path, and mean collision time is its reciprocal. A faster molecule sweeps collision volume more quickly, while a longer free path spaces collisions farther apart.
🧠 Memory hook: Frequency is speed over spacing; time is spacing over speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- z = v_avg/lambda — average collision frequency using compatible mean speed and mean free path
- tau = 1/z = lambda/v_avg — mean time between successive collisions
- z proportional to n_number d² sqrt(T/m) — hard-sphere scaling apart from constants
How to approach it
- 1Write z=v/lambda
- 2Expand only the quantities that change
- 3Check frequency in s⁻¹ or time in seconds
Common slip-ups that cost marks
- •Using rms speed when a formula explicitly requires mean speed without noting approximation
- •Inverting a requested ratio incorrectly
- •Changing pressure without updating number density
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A gas has rms molecular speed 300 m/s at 300 K. What is its rms speed at 1200 K, assuming ideal behavior?
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The root mean square (rms) speed of gas molecules depends on temperature and molar mass, and is a key measure of molecular motion in gases.
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