Question

Pure silicon contains approximately 1.0 × 1016 free electrons per cubic meter.Calculate the mean free time τ for silicon at room temperature.answer 1.5*10^-12b-Your answer in the previous part is much greater than the mean free time for copper given in the textbook. Why, then, does pure silicon have such a high resistivity compared to copper?1-The number of free electrons in copper is much smaller than in pure silicon. Thus, the density of free electrons in silicon is larger. A larger density of current carriers means a higher resistivity.2-The number of free electrons in copper is much smaller than in pure silicon. Thus, the density of free electrons in silicon is larger. A smaller density of current carriers means a higher resistivity.3-The number of free electrons in copper is much larger than in pure silicon. Thus, the density of free electrons in silicon is smaller. A smaller density of current carriers means a higher resistivity.4-The number of free electrons in copper is much larger than in pure silicon. Thus, the density of free electrons in silicon is smaller. A larger density of current carriers means a higher resistivity.

Answer 1

Answer:

(a) 1.5 × 10⁻¹² s

(b)  

3-The number of free electrons in copper is much larger than in pure silicon. Thus, the density of free electrons in silicon is smaller. A smaller density of current carriers means a higher resistivity.

Explanation:

The mean free time can be calculated as;

T = $\frac{m}{ne^2rho}$

= $\frac{9.11*10^{-31}}{1*10^{16}*1.602*10^{-19}*2300}$

= 1.5 × 10⁻¹² s

b).

It is obvious that the value of mean free time of silicon is greater than the copper.

Since; Resistivity = $\frac{1}{free electron density}$  

The value of resistivity is inversely proportional with the free electron density.  THUS, the value of resistivity in the silicon is higher than the copper. As such, the free electron density in the copper is higher than that of silicon (i.e higher resistivity of silicon results to smaller density of current carrier).  

We can therefore conclude that, The number of free electrons in copper is much larger than in pure silicon. Thus, the density of free electrons in silicon is smaller. A smaller density of current carrier means a higher resistivity.