Chapter 29, Problem 67A

To determine

To calculate the longest wavelength of radiation that could excite an electron from the valence band to the conduction band of silicon.

Answer to Problem 67A

The wavelength of radiation that could excite an electron is $1127.27\text{ nm}$ .

Explanation of Solution

Given data:

Energy of forbidden gap of silicon $=1.1\text{ eV}$

The energy-wavelength relation:

  $E=\frac{1240\text{ eV}\cdot \text{nm}}{\lambda }$

Formula used:

  $E=\frac{1240\text{ eV}\cdot \text{nm}}{\lambda }$

  $E$ is the energy of radiation and $\lambda$ is the wavelength of radiation(photon).

Calculation:

As per problem,

For an electron to be excited from the valence band to the conduction band of silicon, $1.1\text{ eV}$ energy is required, which is actually the energy of the forbidden gap.

Calculate the wavelength of radiation using the formula

  $E=\frac{1240\text{ eV}\cdot \text{nm}}{\lambda }$

Rearrange the formula for $\lambda$

  $\lambda =\frac{1240\text{ eV}\cdot \text{nm}}{E}$

Substitute the value $E=1.1\text{ eV}$

  $\begin{array}{l}\lambda =\frac{1240\text{ eV}\cdot \text{nm}}{1.1\text{ eV}}\\ \lambda =1127.27\text{ nm}\end{array}$

Conclusion:

Thus, the wavelength of radiation that could excite an electron is $1127.27\text{ nm}$ .