Question

An aluminum antimonide solid-state laser emits light with a wavelength of 730 nm. Calculate the band gap in joules.

Short answer

The band gap is $2.72\times {10}^{-19}$joules

Step-by-step solution

Given Data

The given wavelength$\mathrm{\lambda }=730\mathrm{nm}\left(\frac{{10}^{-9}\mathrm{m}}{1\mathrm{nm}}\right)=7.30\times {10}^{-7}\mathrm{m}$

Concept Introduction

The formula for bandgap calculation is:

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

Where E is the energy in joules, h isPlanck’s Constant, and c is the speed of light.

Calculation of the band gap

Substituting the given values in the above equation, we get,

$$\begin{gathered} \mathrm{E}=\frac{\mathrm{hc}}{\mathrm{\lambda }} \\ \mathrm{E}=\frac{6.626\times {10}^{-34}\mathrm{J}\times 3.0\times {10}^8\mathrm{m}/\mathrm{s}}{7.30\times {10}^{-7}\mathrm{m}} \\ \mathrm{E}=2.72\times {10}^{-19}\mathrm{J} \end{gathered}$$

Thus, the band gap is$2.72\times {10}^{-19}\mathrm{J}$