Chapter 29, Problem 37GP

To determine

The energy gap between valence and conduction band for diamond.

Answer to Problem 37GP

The energy gap is $\text{5}\text{.49}\text{eV}$ .

Explanation of Solution

Given info:

Wavelength, $\text{λ=226}\text{nm}$ .

Formula used:

It is known that ${\text{E}}_{\text{g}}\text{=}\frac{\text{hc}}{\text{λ}}$

Where,

  ${\text{E}}_{\text{g}}$ is the energy gap.

  $\lambda$ is wavelength.

  $h$ is Planck’s constant, $6.63\times {10}^{-34}J\cdot s$

  $c$ is speed of light, ${\text{3×10}}^{\text{8}}\text{ m/s }$

Calculation:

Substituting the given values is the formula ${\text{E}}_{\text{g}}\text{=}\frac{\text{hc}}{\text{λ}}$

  $\begin{array}{c}{\text{E}}_{\text{g}}\text{=}\frac{\text{(6}{\text{.63×10}}^{\text{-34}}\text{J}\cdot \text{s)×}\left(\text{3}{\text{.0×10}}^{\text{8}}\text{m/s}\right)}{\text{226}\text{nm}}\\ =\frac{\left(1.24\times {10}^3\text{eV}\cdot \text{nm}\right)}{\text{226}\text{nm}}\\ =\text{5}\text{.49}\text{eV}\end{array}$

Conclusion:

The required value is $\text{5}\text{.49}\text{eV}$ .