These four band gaps at 300 K are standard figures worth memorising.

Ascending: Ge < Si < GaAs < GaP, that is (b), (a), (d), (c) — option 1.

Why the ordering makes physical sense. Band gap tracks bond strength and atomic spacing. Germanium's larger atoms bond more weakly, so less energy frees an electron; silicon's tighter lattice raises the gap; the partly ionic gallium compounds raise it further still, and the smaller, more electronegative phosphorus atom in GaP binds more tightly than arsenic in GaAs, giving the largest gap of the four.

What the numbers predict in practice. Intrinsic carrier concentration depends exponentially on the gap,

\(n_{i}\propto \exp\left(-\dfrac{E_{g}}{2kT}\right)\)

so germanium has roughly a thousand times the intrinsic carrier density of silicon and correspondingly larger leakage — the reason germanium devices are limited to about 70 °C while silicon works to 150 °C and beyond. The gap also fixes the cut-in voltage of a junction: about 0.3 V for Ge and 0.7 V for Si.

Direct versus indirect matters as much as the size of the gap. GaAs is direct, so an electron can recombine with a hole and emit a photon without needing a phonon to conserve momentum, which is why lasers and LEDs are made from GaAs and its alloys and not from silicon. The photon energy is set by the gap through

\(\lambda(\mu\text{m})=\dfrac{1.24}{E_{g}(\text{eV})}\)

giving about 870 nm (infrared) for GaAs and about 550 nm (green) for GaP.

Hence, the ascending order of band gap is (b), (a), (d), (c).