Mean free path and collisions
Mean free path is the average distance a molecule travels between collisions, and depends on molecular size and number density.
Why this shows up in the exam
Understanding mean free path helps you answer NEET questions about molecular collisions and transport properties of gases.
How NEET tests this
Learn the idea
Mean free path is the average distance a molecule travels before hitting another molecule; the key insight is that it comes from the geometric cross‑section πd², so λ varies as the inverse of that area.
🧠 Memory hook: If you double the molecular size, the collision ‘target’ area quadruples, so the free path becomes one‑quarter – like a square‑dance step getting tighter.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- λ = 1/(√2 π n d²) (NCERT Eq.)
- n = N/V = number density of molecules
- λ ∝ 1/d² for fixed n
- λ ∝ 1/n (more molecules → shorter path)
- Using PV = NkT, λ = kT/(√2 π d² P)
- Diameter d = 2 r (use d, not r, in the formula)
How to approach it
- 11 Identify which variables are given (d, n, P, T).
- 22 Write the appropriate λ formula from NCERT.
- 33 Keep all other quantities constant and read off the proportionality (e.g., λ ∝ 1/d²).
- 44 If pressure or temperature is given, substitute n = P/(kT) to express λ in those terms.
- 55 Check units and the √2 factor to avoid sign errors.
Worked example — watch it click
The mean free path l for a gas molecule depends upon diameter, d of the molecule as:
- ✅l ∝ 1/d²
- B)l ∝ d
- C)l ∝ d²
- D)l ∝ 1/d
The concept behind this problem
The example asks for the dependence of λ on d, directly testing the student’s grasp of the λ = 1/(√2πnd²) relation and the resulting 1/d² proportionality.
Step by step
- 1From the mean free path formula λ = 1/(√2 π n d²), keeping number density n constant, we see that λ ∝ 1/d².
- 2The mean free path is inversely proportional to the square of the molecular diameter.
Watch out
Students often forget the square on d and answer λ ∝ 1/d, overlooking the geometric cross‑section.
Common slip-ups that cost marks
- •Confusing radius r with diameter d – the formula uses d, not 2r.
- •Omitting the √2 factor leads to a wrong numerical factor but not the proportionality; still keep it in mind.
- •Assuming λ ∝ 1/d (linear) instead of the correct 1/d².
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Practise it
These are real questions from past NEET papers that test this exact idea.
The mean free path for a gas, with molecular diameter d and number density n can be expressed as:
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