Physics

Physics

Problem

In a conductor, if the number of conduction electrons per unit volume is 8.5×1028 m−38.5 \times 10^{28} \text{ m}^{-3} and mean free time is 25 fs25 \text{ fs} (femto second), its approximate resistivity is: ( me=9.1×10−31 kgm_e = 9.1 \times 10^{-31} \text{ kg} ) a. 10−6Ωm10^{-6} \Omega \text{m} b. 10−7Ωm10^{-7} \Omega \text{m} c. 10−8Ωm10^{-8} \Omega \text{m} d. 10−5Ωm10^{-5} \Omega \text{m}
Intuitive explanation

Resistivity connects the microscopic world of electrons to the macroscopic property we measure. The key insight is that resistivity depends on how often electrons collide (captured by mean free time τ\tau) and how many charge carriers are available—use the formula ρ=mene2τ\rho = \frac{m_e}{n e^2 \tau}, which comes from relating conductivity to electron drift and collision dynamics. Plug in the given electron density, mass, and mean free time to find your answer.

Intuitive explanation

Resistivity connects the microscopic world of electrons to the macroscopic property we measure. The key insight is that resistivity depends on how often electrons collide (captured by mean free time τ\tau) and how many charge carriers are available—use the formula ρ=mene2τ\rho = \frac{m_e}{n e^2 \tau}, which comes from relating conductivity to electron drift and collision dynamics. Plug in the given electron density, mass, and mean free time to find your answer.

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