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
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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.