JEE Chemistry The Solid State MCQs Set 23

Chemistry Objective Questions and Answers: The Solid State

Explore reliable objective questions for The Solid State tailored for JEE learners. Utilizing these Chemistry multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

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Multiple Choice Questions

Question 1: A crystal with a ≠ b ≠ c, α = γ = 90°, β ≠ 90° belongs to the:
(a) Tetragonal system
(b) Orthorhombic system
(c) Monoclinic system
(d) Triclinic system
Show Answer & Explanation

Answer: (c) Monoclinic system

Explanation:
1. Monoclinic: a ≠ b ≠ c, α = γ = 90° and β ≠ 90°.
2. Answer: (c)

Teacher's Note:
1. Tetragonal and orthorhombic have all angles 90°.
2. Triclinic has no right angle.

Question 2: The most unsymmetrical crystal system is:
(a) Cubic
(b) Hexagonal
(c) Triclinic
(d) Orthorhombic
Show Answer & Explanation

Answer: (c) Triclinic

Explanation:
1. Triclinic has a ≠ b ≠ c and α ≠ β ≠ γ ≠ 90°, the lowest symmetry.
2. Cubic is the most symmetrical.
3. Answer: (c)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 3: The crystal system of a compound with unit cell dimensions a = 0.387, b = 0.387, c = 0.504 nm and α = β = 90°, γ = 120° is:
(a) Cubic
(b) Hexagonal
(c) Orthorhombic
(d) Rhombohedral
Show Answer & Explanation

Answer: (b) Hexagonal

Explanation:
1. a = b ≠ c with α = β = 90° and γ = 120° is the hexagonal system.
2. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 4: In a simple cubic cell, each corner atom is shared by:
(a) 2 unit cells
(b) 1 unit cell
(c) 8 unit cells
(d) 4 unit cells
Show Answer & Explanation

Answer: (c) 8 unit cells

Explanation:
1. Each corner of a cube is common to 8 cubes, so one-eighth of the atom lies in each cell.
2. Answer: (c)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 5: In a body centred cubic cell, an atom at the body centre is shared by:
(a) 1 unit cell
(b) 2 unit cells
(c) 3 unit cells
(d) 4 unit cells
Show Answer & Explanation

Answer: (a) 1 unit cell

Explanation:
1. The body-centre atom lies wholly inside one unit cell.
2. Answer: (a)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 6: The numbers of atoms present in a unit cell of a monoatomic element of a simple cubic, body centred cubic and face centred cubic lattice respectively are:
(a) 8, 9 and 14
(b) 1, 2 and 4
(c) 4, 5 and 6
(d) 2, 3 and 5
Show Answer & Explanation

Answer: (b) 1, 2 and 4

Explanation:
1. Simple cubic: 8 × 1/8 = 1.
2. bcc: 8 × 1/8 + 1 = 2.
3. fcc: 8 × 1/8 + 6 × 1/2 = 4.
4. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 7: In a body centred cubic unit cell, a metal atom at the centre of the cell is surrounded by how many other metal atoms?
(a) 8
(b) 6
(c) 12
(d) 4
Show Answer & Explanation

Answer: (a) 8

Explanation:
1. The coordination number of bcc is 8: the body-centre atom touches the 8 corner atoms.
2. Answer: (a)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 8: A compound is formed by elements A and B. It crystallises in the cubic structure with A atoms at the corners of the cube and B atoms at the centre of the body. The simplest formula of the compound is:
(a) AB
(b) AB2
(c) A2B
(d) AB4
Show Answer & Explanation

Answer: (a) AB

Explanation:
1. A: 8 × 1/8 = 1; B: 1 at the centre.
2. Formula AB.
3. Answer: (a)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 9: A compound formed by elements A and B has a cubic structure in which A atoms are at the corners of the cube and B atoms are at the face centres. The formula of the compound is:
(a) A4B3
(b) A2B
(c) AB3
(d) A2B3
Show Answer & Explanation

Answer: (c) AB3

Explanation:
1. A: 8 × 1/8 = 1; B: 6 × 1/2 = 3.
2. Formula AB3.
3. Answer: (c)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 10: An element has a bcc structure and 12.08 × 1023 unit cells. The number of atoms in these cells is:
(a) 12.08 × 1023
(b) 24.16 × 1023
(c) 48.38 × 1023
(d) 12.08 × 1022
Show Answer & Explanation

Answer: (b) 24.16 × 1023

Explanation:
1. bcc has 2 atoms per unit cell.
2. Atoms = 2 × 12.08 × 1023 = 24.16 × 1023.
3. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 11: A metal has a bcc structure and the edge length of its unit cell is 3.04 Å. The volume of the unit cell in cm3 is:
(a) 1.6 × 10−21 cm3
(b) 2.81 × 10−23 cm3
(c) 6.02 × 10−23 cm3
(d) 6.6 × 10−24 cm3
Show Answer & Explanation

Answer: (b) 2.81 × 10−23 cm3

Explanation:
1. a = 3.04 × 10−8 cm.
2. V = a3 = 28.1 × 10−24 = 2.81 × 10−23 cm3.
3. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 12: A metal (atomic mass = 50) has a body centred cubic crystal structure. The density of the metal is 5.96 g cm−3. The volume of the unit cell is:
(a) 13.9 × 10−24 cm3
(b) 27.8 × 10−24 cm3
(c) 6.95 × 10−24 cm3
(d) 55.6 × 10−24 cm3
Show Answer & Explanation

Answer: (b) 27.8 × 10−24 cm3

Explanation:
1. Mass of unit cell = 2 × 50/6.022 × 1023 = 1.66 × 10−22 g.
2. V = mass/density = 1.66 × 10−22/5.96 = 27.8 × 10−24 cm3.
3. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 13: An element of density 6.8 g cm−3 occurs in bcc structure with cell edge 290 pm. The number of atoms present in 200 g of the element is:
(a) 2.4 × 1042
(b) 1.2 × 1042
(c) 1.2 × 1024
(d) 2.4 × 1024
Show Answer & Explanation

Answer: (d) 2.4 × 1024

Explanation:
1. Atomic mass M = ρa3NA/2 = 6.8 × 2.439 × 10−23 × 6.022 × 1023/2 = 49.9.
2. Atoms = (200/49.9) × 6.022 × 1023 = 2.4 × 1024.
3. Answer: (d)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 14: The coordination number of the hexagonal close packed (hcp) structure is:
(a) 12
(b) 10
(c) 8
(d) 6
Show Answer & Explanation

Answer: (a) 12

Explanation:
1. Each sphere touches 6 in its layer, 3 above and 3 below: 12.
2. Answer: (a)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 15: The ABAB close packing and ABCABC close packing are respectively called:
(a) hexagonal close packing (hcp) and cubic close packing (ccp)
(b) ccp and hcp
(c) body centred cubic (bcc) packing and hexagonal close packing (hcp)
(d) hcp and bcc
Show Answer & Explanation

Answer: (a) hexagonal close packing (hcp) and cubic close packing (ccp)

Explanation:
1. ABAB repeats after two layers: hcp.
2. ABCABC repeats after three layers: ccp (fcc).
3. Answer: (a)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 16: The vacant space in a bcc unit cell is:
(a) 32%
(b) 10%
(c) 23%
(d) 46%
Show Answer & Explanation

Answer: (a) 32%

Explanation:
1. Packing efficiency of bcc is 68%, so the vacant space is 32%.
2. Answer: (a)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 17: The space occupied by spheres of equal size in three dimensions in both hcp and ccp arrangements is:
(a) 74%
(b) 70%
(c) 60.4%
(d) 52.4%
Show Answer & Explanation

Answer: (a) 74%

Explanation:
1. Both hcp and ccp have a packing efficiency of 74%.
2. Answer: (a)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 18: Which one of the following is NOT a close packing?
(a) hcp
(b) ccp
(c) bcc
(d) fcc
Show Answer & Explanation

Answer: (c) bcc

Explanation:
1. hcp and ccp (fcc) are close packed; bcc (68%) is not.
2. Answer: (c)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 19: Close packing is maximum in the crystal lattice of:
(a) Simple cubic
(b) Face centred
(c) Body centred
(d) Simple cubic and body centred
Show Answer & Explanation

Answer: (b) Face centred

Explanation:
1. Packing efficiency: simple cubic 52.4%, bcc 68%, fcc 74%.
2. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 20: All noble gases crystallise in the ccp structure except:
(a) Helium
(b) Neon
(c) Argon
(d) Krypton
Show Answer & Explanation

Answer: (a) Helium

Explanation:
1. Helium crystallises in hcp; Ne, Ar and Kr form ccp (fcc) solids.
2. Answer: (a)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 21: If the coordination number of an element in its crystal lattice is 8, the packing is:
(a) fcc
(b) hcp
(c) bcc
(d) None of the above
Show Answer & Explanation

Answer: (c) bcc

Explanation:
1. Coordination number 8 is that of bcc; fcc and hcp have 12.
2. Answer: (c)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 22: A tetrahedral void in a crystal implies that:
(a) The shape of the void is tetrahedral
(b) The molecules forming the void are tetrahedral in shape
(c) The void is surrounded tetrahedrally by four spheres
(d) The void is surrounded by six spheres
Show Answer & Explanation

Answer: (c) The void is surrounded tetrahedrally by four spheres

Explanation:
1. A tetrahedral void is the hole at the centre of four spheres placed at the corners of a tetrahedron.
2. Answer: (c)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 23: In a closest packed lattice, the number of octahedral sites as compared to tetrahedral ones is:
(a) Equal
(b) Half
(c) Double
(d) One fourth
Show Answer & Explanation

Answer: (b) Half

Explanation:
1. For N spheres there are N octahedral and 2N tetrahedral voids, so octahedral sites are half of tetrahedral.
2. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 24: The coordination number of a cation occupying an octahedral hole is:
(a) 4
(b) 6
(c) 8
(d) 12
Show Answer & Explanation

Answer: (b) 6

Explanation:
1. An octahedral hole is surrounded by 6 spheres.
2. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 25: The coordination number of a cation occupying a tetrahedral hole is:
(a) 4
(b) 6
(c) 8
(d) 12
Show Answer & Explanation

Answer: (a) 4

Explanation:
1. A tetrahedral hole is surrounded by 4 spheres.
2. Answer: (a)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 26: The number of tetrahedral voids per atom in a crystal lattice is:
(a) 1
(b) 2
(c) 4
(d) 8
Show Answer & Explanation

Answer: (b) 2

Explanation:
1. Closest packing has 2 tetrahedral voids per atom.
2. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 27: If Z is the number of atoms in the unit cell representing the closest packing sequence ABCABC..., the number of tetrahedral voids in the unit cell is equal to:
(a) Z
(b) 2Z
(c) Z/2
(d) Z/4
Show Answer & Explanation

Answer: (b) 2Z

Explanation:
1. Tetrahedral voids = 2 × number of atoms = 2Z.
2. Answer: (b)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

Question 28: For an octahedral arrangement, the lowest radius ratio limit is:
(a) 0.155
(b) 0.732
(c) 0.414
(d) 0.225
Show Answer & Explanation

Answer: (c) 0.414

Explanation:
1. The octahedral range is 0.414 to 0.732.
2. Answer: (c)

Teacher's Note:
1. Use the standard relations of the crystal lattice.
2. Check the answer against the known values for each lattice.

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Multiple Choice Questions (MCQs) for JEE Chemistry The Solid State

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