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Copper drift mobility and scattering time

Short answer

Electron concentration n = (rho N_A)/M = 8.50×10^28 m^-3. Drift mobility mu_d = sigma/(e n) = 4.33×10^-3 m^2/(V·s) (43.3 cm^2/(V·s)). Mean scattering time tau = mu_d m_e/e = 2.46×10^-14 s.

Calculate the drift mobility and mean scattering time of conduction electrons in copper at room temperature, given the conductivity of the copper is 5.9×10⁵ Ω⁻¹ cm⁻¹, the density of copper is 8.96gcm⁻³ and mass is 63.5g/mol.

Use σ=enμd\sigma = e n \mu_d for the mobility and μd=eτ/me\mu_d = e\tau/m_e for the mean scattering time. Copper gives one free electron per atom.

Given: σ=5.9×105 Ω−1cm−1=5.9×107 Ω−1m−1\sigma = 5.9 \times 10^{5}\ \Omega^{-1}\text{cm}^{-1} = 5.9 \times 10^{7}\ \Omega^{-1}\text{m}^{-1}, ρ=8960 kg/m3\rho = 8960\ \text{kg/m}^3, M=63.5 g/molM = 63.5\ \text{g/mol}.

Electron concentration

n=ρNAM=8960×6.022×10230.0635=8.50×1028 m−3n = \frac{\rho N_A}{M} = \frac{8960 \times 6.022 \times 10^{23}}{0.0635} = 8.50 \times 10^{28}\ \text{m}^{-3}

Drift mobility

μd=σen=5.9×1071.602×10−19×8.50×1028=4.33×10−3 m2V−1s−1=43.3 cm2V−1s−1\mu_d = \frac{\sigma}{e n} = \frac{5.9 \times 10^{7}}{1.602 \times 10^{-19} \times 8.50 \times 10^{28}} = 4.33 \times 10^{-3}\ \text{m}^2\text{V}^{-1}\text{s}^{-1} = 43.3\ \text{cm}^2\text{V}^{-1}\text{s}^{-1}

Mean scattering time

τ=μdmee=4.33×10−3×9.109×10−311.602×10−19=2.46×10−14 s\tau = \frac{\mu_d m_e}{e} = \frac{4.33 \times 10^{-3} \times 9.109 \times 10^{-31}}{1.602 \times 10^{-19}} = 2.46 \times 10^{-14}\ \text{s}

Answer: μd≈43.3 cm2V−1s−1\mu_d \approx 43.3\ \text{cm}^2\text{V}^{-1}\text{s}^{-1}, τ≈2.46×10−14 s\tau \approx 2.46 \times 10^{-14}\ \text{s}.

✓ Answer checked by Claude Opus 5.5 (high effort)

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