Gallium nitride (GaN) is a semiconductor with a bandgap Eg=3.2 eV. Calculate the absorption edge of GaN. Express your answer in units of m.

Answer : 0.0000003875

thanks

To calculate the absorption edge of GaN, we need to convert the bandgap energy into a wavelength using the equation:

λ = hc / Eg,

Where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3 x 10^8 m/s), and Eg is the bandgap energy.

First, let's convert the bandgap energy into joules (J) from electron volts (eV):

Eg (J) = Eg (eV) x 1.6 x 10^-19 J/eV.

Plugging in the known values, we get:

Eg (J) = 3.2 eV x 1.6 x 10^-19 J/eV = 5.12 x 10^-19 J.

Now, let's calculate the wavelength using the equation:

λ = hc / Eg.

Plugging in the known values, we get:

λ = (6.626 x 10^-34 J*s x 3 x 10^8 m/s) / (5.12 x 10^-19 J).

After simplifying, the units of J and J*s will cancel out, leaving us with:

λ = (6.626 x 3 x 10^-34 m) / (5.12 x 10^-19).

Evaluating the equation, we get:

λ ≈ 3.568 x 10^-7 m.

Therefore, the absorption edge of GaN is approximately 3.568 x 10^-7 meters.