Q4. How many energy states are there in the valence and conduction bands of a silicon crystal of N atoms, and how many electrons occupy them at 0 K?
8N states in all: 4N in the valence band, filled by the 4N valence electrons, and 4N in the conduction band, empty at 0 K (NCERT page 325).
Q5. What is the longest wavelength of light that can lift an electron across the 0.7 eV gap of germanium?
λ = hc/Eg ≈ 1240/0.7 nm ≈ 1770 nm, in the infrared (reasoned; E = hc/λ from NCERT Chapter 11).
Q6. Why is tin a metal although it is in the same group as carbon, silicon and germanium?
Ordinary white tin (β-Sn) has metallic bands. NCERT’s zero-gap comparison (page 332) is simplified; grey tin (α-Sn), which has a different crystal structure from white tin, is a zero-gap material.
Q7. Give two ways in which semiconductor devices are better than vacuum tubes.
For example: they need no heated cathode or vacuum, and they are small, use little power, work at low voltages and last long with high reliability (NCERT pages 323–324).
Q8. Assertion: at absolute zero, a pure semiconductor behaves like an insulator. Reason: at 0 K its valence band is full and its conduction band empty. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: with no electrons in the conduction band and no vacancies in the valence band, there are no thermally excited carriers in this ideal equilibrium model (NCERT pages 325 and 327).