1. Use the relation between band gap and photon energy

For an LED, the emitted photon energy is approximately equal to the band gap:

$E = E_g = 1.42\ \text{eV}$

Also,

$E = \frac{hc}{\lambda}$

In convenient units,

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

2. Substitute the given band gap

$\lambda = \frac{1240}{1.42}$

$\lambda \approx 873.24\ \text{nm}$

3. Match with the nearest option

The closest option is:

$875\ \text{nm}$

4. Option check

• A: 1243 nm — too large
• B: 875 nm — matches calculated value
• C: 650 nm — too small
• D: 1400 nm — too large

Therefore, the correct answer is Option B.