Question

Carbon(diamond) and silicon have the same covalent crystal structure, yet diamond is transparent while silicon is opaque to visible light. Argue that this should be the case based only on the difference in band gaps roughly 5 eV for diamond in eV is silicon.

Short answer

The value shows that the visible light is absorbed by the silicon but not by diamond.

Step-by-step solution

Determine the formulas

Consider the formula for the energy of the electron as:

$\mathbf{E}\mathbf{=}\frac{\mathrm{hc}}{\lambda }$

Here,$\lambda$ is the wavelength, h is the plank’s constant, and c is the speed of light.

Determine the distance travelled and number of copper ions:

Consider the case of lower range 400 nm as:

$\begin{array}{c}{E}_1=\frac{1240\text{\hspace{0.17em}eV}\cdot \text{nm}}{400\text{\hspace{0.17em}nm}}\\ =3.11\text{\hspace{0.17em}eV}\end{array}$

Solve for the upper value of 750 nm as:

$\begin{array}{c}{E}_2=\frac{1240\text{\hspace{0.17em}eV}\cdot \text{nm}}{750\text{\hspace{0.17em}nm}}\\ =1.66\text{\hspace{0.17em}eV}\end{array}$

The value shows that the visible light is absorbed by the silicon but not by diamond.