Solid state practice · Mixed difficulty

The correct answer is C ($0.905\;\mathop \mathrm{A}\limits^ \circ \;$) because it is calculated using Bragg's Law, $n\lambda = 2d\sin{\theta}$, with the given wavelength and angle.

Option A (1) is correct because in a cubic close-packed (CCP) structure, the number of octahedral voids is equal to the number of atoms in the unit cell.

Option C (1.26) is correct because it accurately calculates the ratio of densities for FCC and BCC structures using their respective unit cell lengths and number of atoms per unit cell.

Option B (63.1 u) is correct because the atomic mass is calculated using the density formula for a face-centered cubic (fcc) unit cell.

Option C (4) is correct because the number of formula units per unit cell is calculated using the formula Z = (V x N x d) / m, resulting in approximately 4.

Option D (MnO) is correct because MnO exhibits antiferromagnetic behavior due to the alignment of magnetic moments in opposite directions.

Option A (0.414) is correct because the ratio of cation to anion in an octahedral close packing is 0.414.

Option B (Quartz) is correct because quartz exhibits piezoelectricity, generating an electric charge under mechanical stress.

Option B (GaAs - Insulator) is the wrong match because GaAs is a semiconductor, not an insulator.

Option C (Molecular solid) is correct because iodine crystals are composed of I2 molecules held together by weak van der Waals forces.

Option B (Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I) is correct because amorphous solids are indeed isotropic, meaning their physical properties are the same in all directions, but this is due to the random arrangement of particles, not simply because physical properties are the same.

Option C (Fcc and bcc) is correct because interchanging $\mathrm{N}{\mathrm{a}^ + }$ and $\mathrm{C}{\mathrm{l}^ - }$ in NaCl results in $\mathrm{N}{\mathrm{a}^ + }$ forming an fcc lattice and $\mathrm{C}{\mathrm{l}^ - }$ forming a bcc lattice.

Option B (Both statement I and statement II are false) is correct because the triclinic system is the most unsymmetrical, and monoclinic systems have two angles equal to 90 degrees.

Option B ($50\%$) is correct because in diamond, half of the tetrahedral voids are occupied by carbon atoms.

Option D is correct because NO, Fe3+, and Fe2+ all possess unpaired electrons, making them paramagnetic.

Option C (Metallic crystals) is correct because metallic crystals are known for their good electrical and thermal conductivity due to the presence of free electrons.

Option B (FCC) is correct because NaCl has a face-centered cubic arrangement of ions.

Option C (Barium titanate) is correct because barium titanate ($BaTiO_3$) is a well-known ferroelectric material.

Option D (In Schottky defect equal number of cations and anions are missing from their lattice sites) is correct because Schottky defects involve the absence of an equal number of cations and anions to maintain electrical neutrality.

Option D ($4 \times {10^{25}}$) is correct because the number of atoms is calculated using the density, cell edge, Avogadro's number, and the number of atoms per unit cell in an FCC crystal.

Option C is correct because Statement I is true as Frenkel defects involve both vacancy and interstitial defects, while Statement II is false as Frenkel defects do not create F-centers.

Option C is correct because the calculation involves finding the volume of a silver atom, then its area, and finally dividing the given surface area by the area of each silver atom.

The correct answer is D (${Ni}(\mathrm{s})$ is repelled from magnetic field and is antiferromagnetic in nature) because Nickel (Ni) is ferromagnetic, not antiferromagnetic, and is attracted to magnetic fields, not repelled.

Option C (Ge) is correct because Germanium (Ge) is a common semiconductor material.

The correct answer is A ($\mathrm{AuC}{\mathrm{u}_3}$) because the gold atoms at the corners contribute 1 atom per unit cell, and the copper atoms at the face centers contribute 3 atoms per unit cell.

Option B (8) is incorrect. The correct answer is A (6). The effective number of carbon atoms in a unit cell of diamond is 8.

Option B (Glass) is correct because glass is an amorphous solid that lacks long-range order and exhibits properties of a supercooled liquid, hence it's considered a pseudo solid.

Option A (Hauy’s law of rationality of indices) is correct because the statement describes Hauy's law.

Option D (Orthorhombic) is correct because the orthorhombic crystal system has four Bravais lattices: primitive, body-centered, face-centered, and end-centered.

The correct answer is A (140) because the radius of the silver atom is calculated using the face-centered cubic (fcc) relationship between the edge length and the radius.