Chapter 29, Problem 69A

To determine

To find the width of the forbidden gap in $\text{eV}$ in the light-emitting diode.

Answer to Problem 69A

The width of the forbidden gap in the light-emitting diode is $\text{2}\text{.25 eV}$ .

Explanation of Solution

Given data:

Wavelength of green light, $\lambda =550\text{ nm}$

Formula used:

The energy-wavelength relation:

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

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

Calculation:

As per problem,

For an electron to be excited from the valence band to the conduction band of silicon,the energy required is actually the width of the forbidden gap.

Calculate the width of forbidden gap using the formula

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

Substitute the value $\lambda =550\text{ nm}$

  $\begin{array}{l}E=\frac{1240\text{ eV}\cdot \text{nm}}{550\text{ nm}}\\ E=2.25\text{ eV}\end{array}$

Conclusion:

Thus, the width of the forbidden gap in the light-emitting diode is $\text{2}\text{.25 eV}$ .