NCERT Class XII - Solid State Chemistry
Integer Type Questions

Important Constants & Information:

Avogadro's Number (NA): 6.022 × 1023 mol-1
Common Crystal Systems: Cubic, Tetragonal, Orthorhombic, Hexagonal, Trigonal, Monoclinic, Triclinic
Coordination Numbers: Simple cubic = 6, BCC = 8, FCC = 12, HCP = 12
Question 1:
In a face-centered cubic (FCC) structure, if the edge length is 400 pm and the atomic radius is 141.4 pm, calculate the packing efficiency as a percentage. Express your answer as the nearest integer.
For FCC: a = 2√2 × r
Packing efficiency = (Volume of atoms / Total volume) × 100
Question 2:
A metallic element crystallizes in a body-centered cubic (BCC) lattice. If the density of the metal is 8.96 g/cm3 and the edge length of the unit cell is 287 pm, calculate the atomic mass of the element in g/mol. Round off to the nearest integer.
Density = (Z × M) / (NA × a3)
where Z = 2 for BCC
Question 3:
In a cubic closest packed (CCP) structure of spheres, if 250 spheres are removed from tetrahedral voids and 125 spheres are removed from octahedral voids, and the remaining structure has 875 spheres in close-packed arrangement, find the total number of tetrahedral voids originally present.
In CCP: Tetrahedral voids = 2N, Octahedral voids = N
where N = number of close-packed spheres
Question 4:
An ionic compound AB has a rock salt structure. If the edge length of the unit cell is 564 pm and the ionic radii are rA+ = 102 pm and rB- = 181 pm, calculate the percentage of space occupied by ions in the unit cell. Express as the nearest integer.
Rock salt structure: a = 2(r+ + r-)
Space occupied = (Volume of all ions / Unit cell volume) × 100
Question 5:
A compound MX2 crystallizes in a fluorite structure. If the edge length is 550 pm and the density is 3.2 g/cm3, calculate the molar mass of the compound MX2 in g/mol. Round to the nearest integer.
Fluorite structure: Z = 4
Density = (Z × M) / (NA × a3)
Question 6:
In a hexagonal close-packed (HCP) structure, the c/a ratio is 1.633. If the atomic radius is 124 pm, calculate the volume of the unit cell in pm3. Express your answer in scientific notation as X × 105 and give the value of X as the nearest integer.
For HCP: a = 2r, c = 1.633a
Volume = (3√3/2) × a2 × c
Question 7:
A crystal of AgCl has a defect where 1015 Ag+ ions are missing from lattice points and the same number of Ag+ ions occupy interstitial sites. If the crystal contains 6.022 × 1020 formula units of AgCl, calculate the percentage of Frenkel defects. Express as the nearest integer value multiplied by 10-3.
Frenkel defect % = (Number of defects / Total lattice points) × 100
Question 8:
In a spinel structure AB2O4, A2+ ions occupy 1/8 of tetrahedral voids and B3+ ions occupy 1/2 of octahedral voids. If there are 32 O2- ions in the unit cell, calculate the total number of cations (A2+ + B3+) in the unit cell.
For 32 O2- ions: Tetrahedral voids = 64, Octahedral voids = 32
Formula: AB2O4
Question 9:
A p-type semiconductor is formed by doping silicon with boron. If 1 ppm (parts per million) of silicon atoms are replaced by boron atoms and the density of silicon is 2.33 g/cm3, calculate the number of boron atoms per cm3. Express your answer in scientific notation as X × 1016 and give X as the nearest integer.
Atomic mass of Si = 28 g/mol
1 ppm = 1 atom per 106 atoms
Question 10:
In an anti-fluorite structure of K2O, if the edge length of the unit cell is 640 pm, calculate the distance between the centers of a K+ ion and its nearest O2- ion in pm. Round to the nearest integer.
Anti-fluorite structure: Cations at tetrahedral voids
Distance = (√3/4) × a
Note: These questions test understanding of crystal structures, unit cells, defects, packing efficiency, density calculations, and coordination chemistry concepts from NCERT Class XII Solid State chapter.