Question

A light-emitting diode (LED) is fabricated using GaAs semiconductor material whose band gap is \( 1.42 \, \text{eV} \). The wavelength of light emitted from the LED is:

• A. \( 650 \, \text{nm} \)
• B. \( 1243 \, \text{nm} \)
• C. \( 875 \, \text{nm} \)
• D. \( 1400 \, \text{nm} \)

Hint:

The wavelength of light emitted by a semiconductor is inversely related to its band gap energy \( E_g \). A smaller band gap corresponds to a longer wavelength, and vice versa.

Answer 1

The Correct Option is C

The wavelength of emitted light is determined using the relationship between the band gap energy \( E_g \) and wavelength \( \lambda \): \[ E_g (\text{eV}) = \frac{1240}{\lambda (\text{nm})}. \] Rearranging for \( \lambda \): \[ \lambda = \frac{1240}{E_g}. \] Step 1: Substitute the Given Values Given: \[ E_g = 1.42 \, \text{eV}. \] Substitute into the equation: \[ \lambda = \frac{1240}{1.42}. \] Perform the calculation: \[ \lambda \approx 875 \, \text{nm}. \] Final Answer: \[ \boxed{875 \, \text{nm}} \]