Chapter 29.1, Problem 7PP

To determine

The number of free electrons in per atom of germaniumat 200 K temperature.

Answer to Problem 7PP

The number of free electrons in per atom of germanium is $2.67\times {10}^{-13}$ .

Explanation of Solution

Given data:

Number of atoms per mole in germanium, $N_a=6.02\times {10}^{23}$ atoms / mole

Atomic mass of germanium, $M=72.6$ g

Density of germanium, $\rho =5.23{\text{ g/cm}}^3$

Number of free electrons per centimeter cube, $f=1.16\times {10}^{10}$

Formula used:

Free electron per atom of germanium,

  $\frac{\text{Free electron}}{\text{atom}}=\left(\frac{1}{N_a}\right)\left(M\right)\left(\frac{1}{\rho }\right)\left(f\right)$

Calculation:

Free electron per atom of germanium,

  $\begin{array}{l}\frac{\text{Free electron}}{\text{atom}}=\left(\frac{1}{N_a}\right)\left(M\right)\left(\frac{1}{\rho }\right)\left(f\right)\\ \frac{\text{Free electron}}{\text{atom}}=\left(\frac{1}{6.02\times {10}^{23}}\right)\left(72.6\right)\left(\frac{1}{5.23}\right)\left(1.16\times {10}^{10}\right)=2.67\times {10}^{-13}\end{array}$

Conclusion:

Hence, the number of free electrons in per atom of germanium is $2.67\times {10}^{-13}$ .