ISRO EC 2025 Q.70: solution and answer

ISRO 2025 · ECQ.70 · 1 mark · MCQ

Select the value closest to the forbidden band in Germanium at 0 K :

(A)
0.78 eV
(B)
1.00 eV
(C)
0.01 eV
(D)
1.21 eV

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Answer and solution

ANSWER

Option (a): $0.78 eV$ is closest to the $0 K$ band gap of germanium ( $\approx 0.74 eV$ ).

Official answer: ASource: ISRO's final answer key of 15 May 2026

The forbidden band is the energy gap $E_{g}$ between the top of the valence band and the bottom of the conduction band.
$E_{g}$ of a semiconductor depends on temperature. It is largest at $0 K$ and falls as temperature rises, roughly as $E_{g} (T) = E_{g} (0) - \frac{α T ^{2}}{T + β}$ .
For germanium the standard values are $E_{g} \approx 0.67 eV$ at $300 K$ and $E_{g} \approx 0.74 eV$ at $0 K$ .
Compare the options with $0.74 eV$ . The value $0.78 eV$ is only $0.04 eV$ away.
The other options are far off. $1.00 eV$ is $0.26 eV$ away. $0.01 eV$ is far too small for a semiconductor gap. $1.21 eV$ is close to the $0 K$ gap of silicon ( $\approx 1.17 eV$ ), not germanium.
So option (a), $0.78 eV$ , is the closest.

KEY IDEA

The band gap of a semiconductor is largest at $0 K$ : about $0.74 eV$ for germanium (versus $0.67 eV$ at room temperature) and about $1.17 eV$ for silicon (versus $1.12 eV$ at room temperature).

WATCH OUT FOR

Using the room-temperature value of $0.67 eV$ for germanium, or picking $1.21 eV$ , which belongs to silicon near $0 K$ , not germanium.

From the ISRO EC 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 3 ISRO Semiconductors questions, with notes