The specific electric resistance is measured at low temperatures on 2 Na samples

Question

The specific electric resistance is measured at low temperatures on 2 Na samples of different impurity concentrations. The idea is to use these measurements to determine the purity of both samples. The following data were obtained from the measurements: The measurements gave the specific resistance of the Na samples with respect to the room temperature value (295K). Determine the specific resistance of the second sample at T = 7 K. Its electric conductivity at 290 K is 2.34 times10^5 (Ohm cm)^-1. Use the Drude model to calculate the relaxation time and the mean free path of the electrons for the second sample at 7 K. Assume that each Na atom contributes one electron to the electron gas. Sketch the temperature dependence of resistance for both samples and comment on how it relates to the purity of the sample (no calculation necessary).

Explanation / Answer

a)

Electrical conductivity is directly proportional to the temperature.

Let K1=2.34* 105 (cm) -1

T1=290K

T2=7K

K1/ K2= T1/T2

Solving for K2

we get,

Electrical conductivity at 7K= 5.648 *103 (cm) -1

Hence, electrical resisitivity will be reciprocal of conductivity = 0.177 *10-3 (cm)

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