Question

An aluminum antimonide solid-state laser emits light with a wavelength of \(730 . \mathrm{nm}\). Calculate the band gap in joules.

Short answer

The band gap energy of the aluminum antimonide solid-state laser that emits light at 730 nm wavelength is approximately \(2.72 \times 10^{-19}\) joules.

Step-by-step solution

Write down the given information and necessary constants

Wavelength of the emitted light, λ = 730 nm = \(7.3 \times 10^{-7}\) m (convert nm to m) Planck's constant, h = \(6.626 \times 10^{-34}\) Js Speed of light in vacuum, c = \(3 \times 10^8\) m/s Our goal is to calculate the bandgap in joules.

Calculate the energy of a photon (E)

We will first find the energy of a photon (E) using the formula: \(E = \dfrac{hc}{\lambda}\) Where E is the energy of the photon, h is the Planck's constant, c is the speed of light in vacuum, and λ is the wavelength of the emitted light.

Plug in the values and calculate the energy

Now we can plug in the values we have to find the energy: \(E = \dfrac{(6.626 \times 10^{-34} \text{ Js}) \times (3 \times 10^8 \text{ m/s})}{(7.3 \times 10^{-7} \text{ m})}\) Upon calculation, we get: \(E = 2.72 \times 10^{-19}\) J

Conclusion

The band gap energy of the aluminum antimonide solid-state laser that emits light at 730 nm wavelength is approximately \(2.72 \times 10^{-19}\) joules.