Solid state practice · Medium

Option B (0.22 to 0.41) is correct because the ideal radius ratio for tetrahedral coordination is in the range of 0.225 to 0.414.

Option D is correct because it accurately counts the total number of atoms in the unit cell, considering contributions from corners and body diagonals.

Option B (Face centred) is correct because Face-centered cubic (fcc) and hexagonal close-packed (hcp) structures have the highest packing efficiency (74%).

Option B (26 % and 32 %) is correct because the percentage of free space in a cubic close-packed (ccp) structure is 26%, and in a body-centered packed (bcc) structure is 32%.

The correct answer is A (${X_4}{Y_3}$) because the formula is determined by the ratio of atoms X and Y in the crystal lattice, considering the occupancy of tetrahedral voids.

Option B ($\frac{1}{4}$) is correct because an edge-center particle is shared by four unit cells.

Option D is correct because it accurately counts the total number of atoms in the unit cell, considering contributions from corners and body diagonals.

Option A (1) is correct because in a face-centered cubic (fcc) structure, there is one octahedral site per sphere (atom).

Option B (anti - fluorite structure) is correct because in an anti-fluorite structure, the cation to anion ratio is 2:1, and the coordination numbers are 4 for the cation and 8 for the anion.

Answer A (AB) is correct because the ratio of atoms A and B in the compound is 1:1, based on their positions in the cubic closed packed structure.

Option D ($AB_2O_2$) is correct because it correctly calculates the ratio of A, B, and O atoms based on their occupancy in the ccp lattice, tetrahedral voids, and octahedral voids, respectively.

Option A ($\mathrm{MnO}$) is correct because $\mathrm{MnO}$ (Manganese(II) oxide) is a classic example of an antiferromagnetic substance where the magnetic moments of adjacent ions are aligned in an antiparallel manner, resulting in zero net magnetic moment.

Option D (Vacancy defect increases the density of the substance) is correct because vacancy defects decrease the density of the substance, not increase it.

Option A ($\frac{a}{2}\mathrm{cm}$) is correct because in an NaCl type structure, the distance between cation and anion is half the cell edge length.

Option D (All) is correct because in ZnS, $Na_2O$, and $CaF_2$ structures, the distance between the nearest cation and anion can be $\frac{\sqrt{3} a}{4}$ when the cation occupies a tetrahedral void.

Option D (phenylacetic acid dimerizes in benzene) is correct because the van't Hoff factor (i) is approximately 0.5, indicating dimerization.

Option B (125 pm) is correct because the radius of the anion is calculated using the rock salt structure relationship with the edge length and cation radius.

Option A is correct because Schottky defects occur in compounds with ions of comparable size to minimize mechanical distortions and charge displacement.

Option C (6) is correct because the radius ratio falls within the range that corresponds to an octahedral coordination number of 6.

Option B (Both Statement I and Statement II are correct but Statement II is not the correct explanation of Statement I) is correct because both statements are true, but the impeding of electron flow is a general property, not the direct cause of decreased conductivity with increased temperature.

Option A (The shift of a positive ion from its normal lattice site to an interstitial site) is correct because the Frenkel defect involves the displacement of an ion (typically a cation) from its lattice site to an interstitial site.

Option C (4) is correct because the percentage of Ni as Ni$^{3+}$ is calculated based on charge balance to maintain neutrality of the compound.

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 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 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 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 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.