Arrange the following materials in the decreasing order of the wavele…

The correct answer is Option (3) → (C), (B), (A), (D)

Note: The given answer is as per the official NTA Answer Key. However, none of the given options appears to be correct, because an n-type semiconductor has the same band gap as the pure semiconductor it is made from, as explained below.

The wavelength for a band gap is that of a photon whose energy equals the gap:

    \( \displaystyle \lambda = \frac{hc}{E_g} \approx \frac{1240}{E_g\,(\mathrm{eV})}\,\mathrm{nm} \)

So decreasing wavelength means increasing band gap.

    \( \text{(B) Ge: } E_g \approx 0.7\,\mathrm{eV}, \ \lambda \approx 1770\,\mathrm{nm} \)
    \( \text{(A) Si: } E_g \approx 1.1\,\mathrm{eV}, \ \lambda \approx 1130\,\mathrm{nm} \)
    \( \text{(D) Diamond: } E_g \approx 5.4\,\mathrm{eV}, \ \lambda \approx 230\,\mathrm{nm} \)

(C) n-type semiconductor — Correct as per NTA; however, it is not correct as a general statement. NTA places it first, taking its “gap” as the donor ionisation energy (about 0.01 eV in Ge, 0.05 eV in Si), which gives (C), (B), (A), (D), Option (3). Doping does not change the band gap, so strictly (C) sits level with its host: (B), then (A) and (C) together, then (D) for silicon, or (B) and (C) together, then (A), then (D) for germanium. Neither order is among the options.

NCERT (2026-27):
Extrinsic Semiconductor – “… The difference in the resistivity of C, Si and Ge depends upon the energy gap between their conduction and valence bands. For C (diamond), Si and Ge, the energy gaps are 5.4 eV, 1.1 eV and 0.7 eV, respectively.”