Question

If the energy band gap is $ 0.72 \, \text{eV} $, what is the wavelength of the emitted photon?

• A. \( 1.1 \, \mu m \)
• B. \( 1.4 \, \mu m \)
• C. \( 1.7 \, \mu m \)
• D. \( 2.0 \, \mu m \)

Hint:

Use the relation \( \lambda (\mu m) = \frac{1.24}{E(\text{eV})} \) for quick approximations of wavelength in micrometers.

Answer 1

The Correct Option is C

Energy of photon is related to wavelength by: \[ E = \frac{hc}{\lambda} \Rightarrow \lambda = \frac{hc}{E} \] Given: \[ E = 0.72 \, \text{eV} = 0.72 \times 1.6 \times 10^{-19} \, \text{J} \] \[ h = 6.62 \times 10^{-34} \, \text{Js}, \quad c = 3 \times 10^8 \, \text{m/s} \] \[ \lambda = \frac{6.62 \times 10^{-34} \times 3 \times 10^8}{0.72 \times 1.6 \times 10^{-19}} \approx 1.7 \, \mu m \]