If a semiconductor photodiode can detect a photon with a maximum wavelength
Question:

If a semiconductor photodiode can detect a photon with a maximum wavelength of $400 \mathrm{~nm}$, then its band gap energy is :

Planck’s constant, $h=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}$.

Speed of light, $\quad c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$

1. (1) $1.1 \mathrm{eV}$

2. (2) $2.0 \mathrm{eV}$

3. (3) $1.5 \mathrm{eV}$

4. (4) $3.1 \mathrm{eV}$

Correct Option: , 4

Solution:

(4)

Given,

Wavelength of photon, $\lambda=400 \mathrm{~nm}$

A photodiode can detect a wavelength corresponding to the energy of band gap. If the signal is having wavelength greater than this value, photodiode cannot detect it.

$\therefore$ Band gap $E_{g}=\frac{h c}{\lambda}=\frac{1237.5}{400}=3.09 \mathrm{eV}$