A) In a Schottky defect, the density of the crystal decreases. This statement is correct. A Schottky defect is a type of point defect in a crystal lattice involving vacancy defects. In this defect, a pair of nearest-neighbor atoms, one cation, and one anion, are missing from their lattice site. Because atoms or ions are missing, the overall density of the crystal lattice decreases.
B) In n-type extrinsic semiconductors, the Fermi level lies close to the valence band. This statement is incorrect. In an n-type extrinsic semiconductor, which is created by doping a pure semiconductor with donor impurities (like arsenic or phosphorus atoms in silicon), the Fermi level actually lies closer to the conduction band, rather than the valence band as the electrons from the donor impurities are easy to excite to the conduction band.
(C) The crystal system with cell dimensions a = b = c, and α = β = γ = 90° is tetragonal. This statement is incorrect. The described crystal system is actually cubic, not tetragonal. In a tetragonal crystal system, a ≠ b = c, and all angles are 90°.
(D) The radius of a cation that can fit into an Octahedral void with 212 pm as the radius of the lattice point is 47.7pm. This statement is incorrect.
In a crystalline structure,
the radius ratio for a cation fitting into an Octahedral void is √2/2 (around 0.414).
Radius ratio = 0.414
r
+ = (radius ratio) x r
-r+ = 0.414 x 212 = 87.8ppm
then the radius of the cation that can fit into the octahedral void would be around 0.414 times 212 pm, which is approximately 87.8 pm, not 47.7pm.