COMEDK · Physics · 30. Semiconductors

An LED is constructed from a \(p\)-\(n\) junction diode using GaAsP. The energy gap is \(1.9 \mathrm{~eV}\). The wavelength of the light emitted will be equal to

A \(654 ~\mathop A\limits^o\)
B \(654 \mathrm{~nm}\)
C \(654 \times 10^{-11} \mathrm{~m}\)
D \(10.4 \times 10^{-26} \mathrm{~m}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(654 \mathrm{~nm}\)

Step-by-step Solution

Detailed explanation

The energy of the emitted photon is given by the energy gap \(E_g\) of the semiconductor material. \(E_g = 1.9 \text{ eV} = 1.9 \times 1.6 \times 10^{-19} \text{ J} = 3.04 \times 10^{-19} \text{ J}\) The relationship between the energy of a photon and its wavelength \(\lambda\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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