Solid state practice · Mixed difficulty

Option B (Cubic) is correct because cubic voids are formed by the arrangement of eight spheres, making them the largest among the given options.

Option B ($1.5 \times {10^{23}}$) is correct because it is calculated by dividing the number of moles of NaCl by the number of NaCl units per unit cell and multiplying by Avogadro's number.

Option C (4) is correct because in a diamond structure, each carbon atom contributes a specific fraction to the unit cell, resulting in a total of 4 effective carbon atoms.

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

Option D ($1 \times {10^{20}}$) is correct because it is calculated by dividing the total mass by the mass of one unit cell and accounting for unit conversions.

Option A is correct because quartz is a crystalline form of silica ($SiO_2$).

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 A ($27\,g/mol$) is correct because the molar mass can be calculated from the density, edge length, and the number of atoms per unit cell for an FCC lattice.

Option D (6, 12, 8) is correct because the coordination numbers for simple cubic, FCC, and BCC lattices are 6, 12, and 8, respectively.

Option C is correct because Bragg's Law (nλ = 2dsinθ) is used to calculate the interplanar spacing (d), and the calculation yields approximately 0.905 Å.

Option C (155.9 pm) is correct because it's the calculated radius for a BCC structure with the given edge length.

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 C ((A) is correct but (R) is not correct) is correct because FCC is more closely packed than BCC, but the packing fraction of FCC is not double that of BCC.

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 ($\alpha = \beta = \gamma = {90^0}$).

Option D (All of these) is correct because Schottky defects are commonly observed in ionic compounds with high coordination numbers, such as NaCl, KCl, and CsCl.

Option A ($\uparrow \mathrm{ } \uparrow \mathrm{ } \uparrow \mathrm{ } \uparrow$) is correct because ferromagnetism arises from the parallel alignment of electron spins in the same direction.

Option C (Silicon) is correct because amorphous silicon is commonly used as a photovoltaic material to convert sunlight into electricity.

Option B (Between 0.73 and 0.41) is correct. The correct range is between 0.41 and 0.73 because a coordination number of 6 corresponds to an octahedral geometry, and the radius ratio for octahedral geometry falls within that range.

Option A (four and its unit cell has eight carbon atoms) is correct because in diamond, each carbon atom is tetrahedrally bonded to four other carbon atoms, and the unit cell contains eight carbon atoms.

Option D (All are correct answer) is correct because Zinc is added to the Ag-Pb alloy, then cooled, forming immiscible layers X and Y, where X contains Zn and Ag, and Y contains Pb and Ag with less silver than X.

Option D ($100 \%$) is correct because in a simple cubic unit cell, atoms are present only at the corners, and the edge is fully occupied by the atoms.

Option D (All of the above) is correct because the yellow color and conducting nature of heated ZnO are due to metal excess defects, interstitial cations, and trapped electrons.

Option B (0.255 to 0.414) is correct because the limiting radius ratio for tetrahedral coordination is in the range of 0.225 to 0.414. The closest option is 0.255 to 0.414.

Option D ($1: 1$) is correct because Graham's law of effusion relates the rate of effusion to the square root of the molar mass. By comparing the effusion rates of the mixture and gas X, and using the given molecular mass of X, the mole ratio of H2 and CH4 can be determined to be 1:1.

Option A (The shift of a positive ion from its normal lattice site to an interstitial site) is correct because this is the defining characteristic of a Frenkel defect.

Option D (Piezoelectricity) is correct because piezoelectricity is the phenomenon where certain crystals generate an electric signal when pressure is applied.

Option A ($ABC$) is correct because if C forms CCP, A occupies all octahedral voids, and B occupies half the tetrahedral voids, the ratio of A:B:C is 1:1:1.