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UPCET / UPSEE Mean Free Path — practice questions

Explore 4 free Mean Free Path questions in UPCET / UPSEE Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Mean Free Path questions and exercises with answers

Showing questions 1–4 of 4.

The **mean free path** of a gas molecule is:Read the answer and worked solution →Mean free path of nitrogen at STP (d = 324 pm) is approximately:Read the answer and worked solution →If P is doubled at constant T (compress gas isothermally), the mean free path:Read the answer and worked solution →If the mean free path of N₂ at 1 atm is ~80 nm, what is it at 0.01 atm (same T)?Read the answer and worked solution →

Worked practice questions

The **mean free path** of a gas molecule is:

  1. The total distance travelled in 1 second
  2. The average distance between two successive collisions
  3. The diameter of the molecule
  4. The size of the container
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Correct answer: B. The average distance between two successive collisions

Mean free path λ = average distance a molecule travels between successive collisions. $\lambda = 1/(\sqrt 2 \pi d^2 \cdot N/V)$ for molecular diameter $d$ and number density $N/V$.

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Mean free path of nitrogen at STP (d = 324 pm) is approximately:

  1. ~$10^{-9}$ m
  2. ~$10^{-7}$ m (≈ 80 nm; ~250× molecular diameter)
  3. ~$10^{-3}$ m
  4. ~$1$ m
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Correct answer: B. ~$10^{-7}$ m (≈ 80 nm; ~250× molecular diameter)

$\lambda = k_B T / (\sqrt 2 \pi d^2 P) = (1.38\times10^{-23})(273)/(\sqrt 2 \pi (324\times10^{-12})^2 (1.01\times10^5)) \approx 8\times10^{-8}$ m. About 250× the molecular diameter.

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If P is doubled at constant T (compress gas isothermally), the mean free path:

  1. Doubles
  2. Halves (λ ∝ 1/N/V ∝ T/P)
  3. Quadruples
  4. Stays same
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Correct answer: B. Halves (λ ∝ 1/N/V ∝ T/P)

$\lambda = k_B T /(\sqrt 2 \pi d^2 P)$ ⇒ $\lambda \propto T/P$ (at fixed $d$). Doubling $P$ halves λ.

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