Solid state practice · Easy

Option B (6) is correct because the radius ratio of Na+ to Cl- falls within the range that favors an octahedral coordination number.

Option B (2 unit cells) is correct because an atom at the face center of a face-centered cubic (FCC) unit cell is shared by two adjacent unit cells.

Option A is correct because solid $CO_2$ (dry ice) consists of individual $CO_2$ molecules held together by weak van der Waals forces, which is characteristic of molecular crystals.

Option B ($CsCl\,type$) is correct because the radius ratio falls within the range for CsCl structure.

Option A (Ionic crystal) is correct because LiF is formed by the electrostatic attraction between Li+ and F- ions, which is characteristic of ionic bonding.

Option B (Quartz) is correct because quartz exhibits piezoelectricity, which means it generates an electric charge when subjected to mechanical stress.

Option D (All) is correct because Diamond and Graphite are well-known covalent solids, and $Fe_2O_3$ can also exhibit covalent character due to the electronegativity difference between Fe and O.

Option A is correct because the radius ratio (r+/r-) falls within the range for a coordination number of 6, which is typical for octahedral structures.

Option D (All of these) is correct because solids are characterized by incompressibility, mechanical strength, and crystalline nature.

Option C ($32\%$) is correct because the packing efficiency of a bcc unit cell is 68%, so the vacant space is 100% - 68% = 32%.

Option D is the correct statement because it accurately describes the crystal parameters for a hexagonal unit cell.

Option B ($A{B_3}$) is correct because A atoms at the corners contribute 1/8 each, totaling 1 A atom, and B atoms at the face centers contribute 1/2 each, totaling 3 B atoms.

Option B is correct because in an orthorhombic system, the axial ratios are unequal ($a \ne b \ne c$), but all the axial angles are equal to 90 degrees ($\alpha = \beta = \gamma = 90^0$).

Option C (Are arranged in ccp) is correct because in the antifluorite structure, the positions of cations and anions are reversed compared to the fluorite structure. The negative ions (anions) form the ccp lattice.

Option D (A Frenkel defect is formed when an ion is displaced from its lattice site to an interstitial site) is correct because this is the definition of a Frenkel defect.

Option C (Frenkel defect) is correct because Frenkel defects involve ions moving within the lattice, so the mass and volume remain constant, thus density remains unchanged.

Option A ($\mathrm{ }1.8574;\mathop \mathrm{A}\limits^ \circ$) is correct because it's the calculated radius for a BCC lattice given the edge length.

Option D (8) is correct because in a body-centered cubic (bcc) lattice, each atom is surrounded by 8 nearest neighbors, giving it a coordination number of 8.

Option D (Molecular) is correct because molecular solids have low melting points and are poor conductors of heat and electricity due to weak intermolecular forces.

Option C (The density of the overall crystal remains the same) is the wrong statement. Schottky defects involve missing ions, which reduces the density.

Option C (8) is correct because in the fluorite structure ($CaF_2$), each $Ca^{2+}$ ion is surrounded by 8 $F^-$ ions, giving it a coordination number of 8.

Option D ($F{e_3}{O_4}$) is correct because it is a well-known example of a ferrimagnetic substance, exhibiting a net magnetic moment due to unequal alignment of magnetic moments.

Option A ($f + c = e + 2$) is correct because it represents Euler's formula for polyhedra, relating the number of faces, edges, and corners in a crystal.

Option C (Minimum) is correct because atoms in a crystal lattice arrange themselves to minimize potential energy, leading to a stable configuration.

Option A ($\frac{\pi }{{3\sqrt 2 }}$) is correct because it is the formula for packing efficiency in a face-centered cubic (fcc) lattice, derived from the ratio of the volume occupied by atoms to the total volume of the unit cell.

Option C (Molecular crystal) is correct because wax is composed of large organic molecules held together by weak intermolecular forces.

Option A ($f + c = e + 2$) is correct because it represents Euler's formula for polyhedra, which relates the number of faces (f), edges (e), and vertices (c) in a crystal.

Option C (Both (1) and (2)) is correct because doping with either Arsenic (As) or Boron (B) increases the conductivity of Germanium (Ge) and Silicon (Si).

Option D (Van der Waals’ forces) is correct because solid hydrogen consists of H2 molecules held together by weak van der Waals forces at very low temperatures.

Option A ($a \ne b \ne c,\alpha = \beta = \gamma = {90^0}$) is correct because the orthorhombic crystal system is defined by having three unequal axes ($a \ne b \ne c$) and all angles equal to 90 degrees ($\alpha = \beta = \gamma = {90^0}$).