Chapter 29.1, Problem 11PP

To determine

The number of free electrons per atom at room temperature in silicon atom.

Answer to Problem 11PP

The number of free electrons per atom in silicon is $3.78\times {10}^{-18}$ and the temperature in Celsius is −73.

Explanation of Solution

Given data:

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

Atomic mass of silicon, $M=28.09$

Density of silicon, $\rho =2.33{\text{ g/cm}}^3$

Number of free electrons per centimeter cube, $f= 1.89\times {10}^5$

Formula used:

Number of free electrons in 1 ${\text{cm}}^3$ of gold,

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

Calculation:

Free electron per atom of silicon,

  $\begin{array}{l}\frac{\text{Free electron}}{\text{atom}}=\left(\frac{1}{N_a}\right)\left(M\right)\left(\frac{1}{\rho }\right)\left(f\right)\\ \frac{\text{Free electron}}{\text{atom}}=\left(\frac{1}{6.02\times {10}^{23}}\right)\left(28.09\right)\left(\frac{1}{2.33}\right)\left(1.89\times {10}^5\right)=3.78\times {10}^{-18}\end{array}$

Temperature in Celsius = Temperature in Kelvin − 273 = 200 − 273 = −73celsius

Conclusion:

Hence, the number of free electrons per atom in silicon is $3.78\times {10}^{-18}$ and the temperature in Celsius is −73.