1. Physical idea

In a reverse-biased $P\!- N$ junction, if light falls on the junction and the reverse current increases, it means photons are generating electron-hole pairs.

For this to happen, the photon energy must be at least equal to the band gap energy:

$E_{\text{photon}} \ge E_g$

Given that this happens for light of wavelength $\lambda \le 621\,\text{nm}$, the threshold wavelength is approximately

$\lambda_0 = 621\,\text{nm}$

So,

$E_g \approx \frac{hc}{\lambda_0}$

2. Use the standard relation

For photon energy in electron-volts:

$E(\text{eV}) = \frac{1240}{\lambda(\text{nm})}$

Thus,

$E_g \approx \frac{1240}{621} \text{ eV}$

3. Calculate

$E_g \approx 1.997 \text{ eV} \approx 2 \text{ eV}$

4. Match with the options

• A: $1\,\text{eV}$
• B: $4\,\text{eV}$
• C: $0.5\,\text{eV}$
• D: $2\,\text{eV}$

Hence, the correct option is:

$\boxed{D\;:\;2\,\text{eV}}$

5. Comparison with stored answer

Stored correct answer: $D$

My derived answer is also $D$, so they agree.