Question

A cc camera is fabricated using a semiconducting material having a band gap of 3 eV. The wavelength of light it can detect is nearly

• A. 210 nm
• B. 546 nm
• C. 413 nm
• D. 345 nm

Hint:

To estimate wavelength from energy in eV, use the formula: \( \lambda(nm}) \approx \frac{1240}{E(eV})} \).

Answer 1

The Correct Option is C

Step 1: Use the relation between energy and wavelength.
The energy of a photon is related to its wavelength by: \[ E = \frac{hc}{\lambda} \Rightarrow \lambda = \frac{hc}{E} \] 
Where:
Step 2: Calculate the wavelength.
\[ \lambda = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{3 \times 1.6 \times 10^{-19}} = \frac{1.9878 \times 10^{-25}}{4.8 \times 10^{-19}} \approx 4.14 \times 10^{-7} \, \text{m} = 414 \, \text{nm} \] Step 3: Select the closest option.
The wavelength is approximately 413 nm, which matches option (3).