---
title: "Mean free path for 53 cm²/V·s mobility"
subject: "Electrical Engineering Material"
chapter: 2
key: "semester_3/electrical_engineering_material:mean-free-path-53-mobility"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/mean-free-path-53-mobility
site: BCT Engineering
---

# Mean free path for 53 cm²/V·s mobility

Electrical Engineering Material · Chapter 2: Free Electron Theory of Conduction in Metal

- Asked in: 2068 Chaitra, 4 marks
- Video: [Important terms in Free electron theory (Drift velocity, Mean free path, Relaxation time) PHYSICS](https://www.youtube.com/watch?v=CI1R3r4sfDY) — Gautam Varde
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/mean-free-path-53-mobility
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-2

## Question

Conduction electrons with drift mobility of 53cm²V⁻¹s⁻¹ and mean speed of 2.2 × 10⁶ms⁻¹ collides. Calculate the mean free path of electrons between collision.

## Short answer

Mean free time τ = μ_d m_e/e = 3.01×10⁻¹⁴ s. Mean free path λ = u τ = 6.63×10⁻⁸ m (66.3 nm).

## Answer

The drift mobility is related to the mean free time $\tau$ by $\mu_d = e\tau/m_e$, and the mean free path is $\lambda = u\tau$, where $u$ is the mean speed.

**Given:** $\mu_d = 53\ \text{cm}^2\text{V}^{-1}\text{s}^{-1} = 53 \times 10^{-4}\ \text{m}^2\text{V}^{-1}\text{s}^{-1}$, $u = 2.2 \times 10^{6}\ \text{m/s}$.

#### Mean free time

$$
\tau = \frac{\mu_d m_e}{e} = \frac{53 \times 10^{-4} \times 9.109 \times 10^{-31}}{1.602 \times 10^{-19}} = 3.01 \times 10^{-14}\ \text{s}
$$

#### Mean free path

$$
\lambda = u\tau = 2.2 \times 10^{6} \times 3.01 \times 10^{-14} = 6.63 \times 10^{-8}\ \text{m} \approx 66.3\ \text{nm}
$$

This is a few hundred atomic spacings, so electrons pass many ions before being scattered.

**Answer:** $\lambda \approx 6.63 \times 10^{-8}\ \text{m} = 66.3\ \text{nm}$ ($\tau = 3.01 \times 10^{-14}$ s).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Mean free time from mobility is
   A. τ = e/(μ_d m_e)
   B. τ = μ_d m_e/e
   C. τ = μ_d e/m_e
   D. τ = μ_d/(m_e e)
   Answer: B. From μ_d = eτ/m_e. (Key point: Mobility and τ)

2. 53 cm^2/V/s equals
   A. 53e-4 m^2/V/s
   B. 53e-2 m^2/V/s
   C. 53e4 m^2/V/s
   D. 53e-6 m^2/V/s
   Answer: A. 1 cm^2 = 1e-4 m^2. (Key point: Unit conversion)

3. λ is
   A. u/τ
   B. τ/u
   C. u τ^2
   D. u τ
   Answer: D. Speed times time between collisions. (Key point: Mean free path)

4. The mean free path is about
   A. 6.63 nm
   B. 663 nm
   C. 66.3 nm
   D. 3.01e-14 m
   Answer: C. τ = 3.01e-14 s, λ = 2.2e6 x 3.01e-14 = 6.63e-8 m. (Key point: Result)

## Related in Electrical Engineering Material

- [Mean free path from drift mobility](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Amean-free-path-43-mobility) — Electrical Engineering Material, chapter 2, asked 4×
- [Drift mobility of electrons in potassium](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Apotassium-drift-mobility-39-5) — Electrical Engineering Material, chapter 2, asked 2×
- [Copper drift mobility from scattering cross-section](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Acopper-mobility-from-cross-section) — Electrical Engineering Material, chapter 2
- [Copper drift mobility and scattering time](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Acopper-mobility-scattering-time) — Electrical Engineering Material, chapter 2
- [Relaxation time and mean free path](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Arelaxation-time-mean-free-path) — Electrical Engineering Material, chapter 2, asked 4×
- [Si polarizability with 6×10²² electrons/cm³](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Asi-polarizability-6e22) — Electrical Engineering Material, chapter 3

## Related in other subjects

- [Drift speed of electrons, 10 A](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adrift-speed-copper-ten-amp) — Engineering Physics, chapter 8, asked 2×
- [Drift speed of electrons, 20 A](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adrift-speed-copper-twenty-amp) — Engineering Physics, chapter 8, asked 2×
- [Drift velocity of electrons in copper](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adrift-velocity-copper-two-hundred-amp) — Engineering Physics, chapter 8
- [Drift speed in copper wire, 17 mA](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adrift-speed-copper-seventeen-ma) — Engineering Physics, chapter 8