Solid State - MCQs with Explanations

1. In a face-centred cubic lattice, a unit cell is shared equally by how many unit cells?

• (a) 2
• (b) 4
• (c) 6
• (d) 8

Correct Answer: (c)

Explanation: In a face-centred cubic (fcc) arrangement, each face is shared equally by two unit cells. Since there are six faces, the unit cell is shared with six adjacent cells.

2. Which is not the correct statement for ionic solids in which positive and negative ions are held by strong electrostatic attractive forces?

• (a) The radius ratio $(r^{+}/r^{-})$ increases as coordination number increases.
• (b) As the difference in size of ions increases, coordination number increases.
• (c) When coordination number is eight, $r^{+}/r^{-}$ ratio lies between 0.225 to 0.414.
• (d) In ionic solid of the type AX (ZnS, Wurtzite), the coordination number of $Zn^{2+}$ and $S^{2-}$ respectively are 4 and 4.

Correct Answer: (c)

Explanation: For a coordination number of 8, the radius ratio $(r^{+}/r^{-})$ should actually lie between 0.732 and 1.000, not 0.225 to 0.414.

3. The number of formula units in the crystal of NaCl, ZnS and $MgO (r_c/r_a = 0.5)$ will have the ratio:

• (a) 4:6:2
• (b) 4:4:4
• (c) 4:2:6
• (d) 6:6:4

Correct Answer: (b)

Explanation: NaCl has 4 formula units per unit cell. ZnS also has 4 formula units. MgO, with a radius ratio of 0.5, adopts the NaCl type structure and thus also has 4 formula units, resulting in a 4:4:4 ratio.

4. Which of the following statements is not true about NaCl structure?

• (a) Each unit cell contains four NaCl molecules.
• (b) $Cl^{-}$ ions have coordination number six.
• (c) $Na^{+}$ ions have coordination number four.
• (d) $Cl^{-}$ ions are in fcc arrangement.

Correct Answer: (c)

Explanation: In the rock salt (NaCl) structure, both $Na^{+}$ and $Cl^{-}$ ions have a coordination number of six.

5. How many six-fold axis of symmetry does a hexagonal close packing have?

• (a) 2
• (b) 3
• (c) 1
• (d) 4

Correct Answer: (c)

Explanation: A hexagonal close packing (hcp) has only one six-fold axis of symmetry, which is the imaginary line joining the centers of the hexagonal faces.

6. How many unit cells are present in 39 g of potassium that crystallises in body-centred cubic structure?

• (a) $N_{A}$
• (b) $N_{A}/4$
• (c) 0.5 $N_{A}$
• (d) 0.75 $N_{A}$

Correct Answer: (c)

Explanation: 39 g of K corresponds to 1 mole or $N_A$ atoms. Since a bcc unit cell contains 2 atoms ($Z=2$), the number of unit cells is $N_A/2 = 0.5 N_A$.

7. In fcc arrangement of A and B atoms, where A atoms are at the corners and B atoms at the face centres, if two atoms are missing from corners, the simplest formula is:

• (a) $A_{7}B_{6}$
• (b) $A_{6}B_{7}$
• (c) $A_{7}B_{24}$
• (d) $AB_{4}$

Correct Answer: (d)

Explanation: A-atoms occupy 6 corners (6 × 1/8 = 3/4 atoms). B-atoms occupy 6 face centers (6 × 1/2 = 3 atoms). The ratio A:B is 3/4 : 3, which simplifies to 1:4, giving the formula $AB_4$.

8. Which of the following formulae is consistent with the unit cell of the rhenium oxide compound shown? (Rhenium at corners, Oxygen at edge centers)

• (a) $ReO_{3}$
• (b) $Re_{2}O_{3}$
• (c) $ReO_{6}$
• (d) ReO

Correct Answer: (a)

Explanation: There are 8 Rhenium atoms at corners (8 × 1/8 = 1) and 12 Oxygen atoms at edge centers (12 × 1/4 = 3). Thus, the formula is $ReO_3$.

9. Which of the following statements about amorphous solids is incorrect?

• (a) They melt over a range of temperature.
• (b) They are anisotropic.
• (c) There is no orderly arrangement of particles.
• (d) They are rigid and incompressible.

Correct Answer: (b)

Explanation: Amorphous solids are isotropic, meaning their physical properties are the same in all directions.

10. Non-stoichiometric metal deficiency is shown in the salts of:

• (a) all metals
• (b) alkali metals only
• (c) alkaline earth metals only
• (d) transition metals only.

Correct Answer: (d)

Explanation: This defect is common in transition metals because they can exhibit variable oxidation states, allowing them to maintain electrical neutrality when some metal ions are missing.

11. Ionic solids with Schottky defects contain in their structure:

• (a) equal number of cation and anion vacancies
• (b) interstitial anions and anion vacancies
• (c) cation vacancies only
• (d) cation vacancies and interstitial cations.

Correct Answer: (a)

Explanation: Schottky defect is a vacancy defect where an equal number of cations and anions are missing from the lattice to maintain electrical neutrality.

12. Which of the following crystals does not exhibit Frenkel defect?

• (a) KBr
• (b) AgBr
• (c) AgCl
• (d) ZnS

Correct Answer: (a)

Explanation: KBr exhibits Schottky defects because the size difference between the cation and anion is relatively small. AgBr, AgCl, and ZnS exhibit Frenkel defects.

13. Which of the following defects decrease the density? (I. Interstitial, II. Vacancy, III. Frenkel, IV. Schottky)

• (a) I and IV
• (b) II and IV
• (c) III and IV
• (d) I, II and III

Correct Answer: (b)

Explanation: Vacancy and Schottky defects involve missing ions while the volume remains constant, thus decreasing the mass and the density.

14. Element Y (anions) makes ccp and X (cations) occupy all octahedral voids. The formula is:

• (a) XY
• (b) $X_{2}Y$
• (c) $XY_{2}$
• (d) $XY_{3}$

Correct Answer: (a)

Explanation: In a ccp lattice, the number of octahedral voids equals the number of lattice atoms. If all octahedral voids are filled by X and the lattice is Y, the ratio is 1:1.

15. Graphite is a soft solid lubricant difficult to melt because:

• (a) is non-crystalline
• (b) is allotrope of diamond
• (c) has variable molecular mass
• (d) has carbon atoms in large plates with weak interplate bonds.

Correct Answer: (d)

Explanation: Graphite consists of layered plates where atoms are strongly bonded within the layer but held by weak van der Waals forces between layers, allowing them to slide.

16. Which crystal has the highest melting point?

• (a) Ionic crystal
• (b) Molecular crystal
• (c) Covalent crystal
• (d) Metallic crystal

Correct Answer: (c)

Explanation: Covalent network crystals (like diamond) have the highest melting points because of their extensive strong 3D covalent bonding.

17. The total number of atoms required to form a unit cell of bcc lattice will be:

• (a) 6
• (b) 8
• (c) 9
• (d) 12

Correct Answer: (c)

Explanation: To physically construct the bcc unit cell, you need 8 atoms for the corners and 1 atom for the body center, totaling 9.

18. A unit cell with $a = b = c$ and $\alpha = \beta = \gamma = 90^{\circ}$ represents which system?

• (a) Cubic
• (b) Orthorhombic
• (c) Tetragonal
• (d) Trigonal

Correct Answer: (a)

Explanation: These dimensions define the cubic crystal system.

19. Which of the following is a pseudo solid?

• (a) $CaF_{2}$
• (b) Glass
• (c) NaCl
• (d) All of these

Correct Answer: (b)

Explanation: Glass is an amorphous solid, often referred to as a pseudo solid or supercooled liquid.

20. Atoms A at corners, B at center of cube. Formula is:

• (a) $A_{2}B_{3}$
• (b) $AB_{2}$
• (c) $AB_{3}$
• (d) AB

Correct Answer: (d)

Explanation: A-atoms contribute 8 × 1/8 = 1. B-atom at the center contributes 1. The formula is AB.

21. Edge length of fcc is 508 pm. Radius of cation is 110 pm. Radius of anion is:

• (a) 110 pm
• (b) 144 pm
• (c) 618 pm
• (d) 398 pm

Correct Answer: (b)

Explanation: For an fcc unit cell (NaCl type), edge length $a = 2(r^+ + r^-)$. So, $508 = 2(110 + r^-)$, which gives $r^- = 144$ pm.

22. Metal bcc, edge 300 pm, molar mass $50 \text{ g mol}^{-1}$. Density ($in \text{ g cm}^{-3}$) is:

• (a) 3.1
• (b) 6.2
• (c) 9.3
• (d) 12.4

Correct Answer: (b)

Explanation: $\rho = \frac{Z \times M}{N_A \times a^3}$. For bcc, $Z=2$. Using $M=50$ and $a=300 \times 10^{-10} \text{ cm}$, the density is approx $6.15 \approx 6.2 \text{ g cm}^{-3}$.

23. The fcc crystal contains how many atoms in each unit cell?

• (a) 6
• (b) 8
• (c) 4
• (d) 5

Correct Answer: (c)

Explanation: In fcc, there is 1 atom from corners (8 × 1/8) and 3 atoms from faces (6 × 1/2), totaling 4 atoms.

24. Which solid will have weakest intermolecular forces?

• (a) Ice
• (b) Phosphorus
• (c) Naphthalene
• (d) Sodium fluoride

Correct Answer: (a)

Explanation: Ice has the lowest melting point among these, indicating the weakest intermolecular forces.

25. In cubic close packing (ccp) arrangement, the pattern is:

• (a) AB, AB, AB ...
• (b) AB, ABC, AB ...
• (c) ABC, ABC, ABC ...
• (d) none of these.

Correct Answer: (c)

Explanation: The ccp arrangement is characterized by an ABCABC pattern of layers.

26. Schottky defect is likely to be found in:

• (a) AgI
• (b) NaCl
• (c) ZnS
• (d) ZnO

Correct Answer: (b)

Explanation: NaCl has ions of similar size and high coordination numbers, typical of solids that exhibit Schottky defects.

27. Frenkel defect is generally observed in:

• (a) AgBr
• (b) AgI
• (c) ZnS
• (d) all of these

Correct Answer: (d)

Explanation: All these compounds exhibit Frenkel defects because there is a large difference in ion sizes, allowing the smaller ion to move into an interstitial site.

28. As a result of Frenkel defect:

• (a) there is no effect on the density
• (b) there is no effect on the conductivity
• (c) there is no effect on the dielectric constant
• (d) there is no effect on all the three above.

Correct Answer: (a)

Explanation: Ions only move within the lattice and do not leave it, so the mass and volume (and thus density) remain unchanged.

29. TlCl, density $9.0 \text{ g cm}^{-3}$, edge $3.85 \times 10^{-8} \text{ cm}$. What is the geometry?

• (a) Simple cubic
• (b) bcc
• (c) fcc
• (d) hcp

Correct Answer: (a)

Explanation: Calculating the number of atoms per unit cell ($Z$) using the density formula yields $Z \approx 1$, indicating a simple cubic arrangement.

30. Silver fcc, density 10.5, edge $4.09 \times 10^{-x} \text{ cm}$. The value of x is:

• (a) 6
• (b) 2
• (c) 4
• (d) 8

Correct Answer: (d)

Explanation: Solving the density formula for $a$ gives $a = 4.09 \times 10^{-8} \text{ cm}$. Thus, $x=8$.

31. Metal fcc, edge 404 pm, density 2.72. The molar mass is:

• (a) $27 \text{ g mol}^{-1}$
• (b) $20 \text{ g mol}^{-1}$
• (c) $40 \text{ g mol}^{-1}$
• (d) $30 \text{ g mol}^{-1}$

Correct Answer: (a)

Explanation: Rearranging the density formula to solve for $M$ with $Z=4$ for fcc yields $M = 27 \text{ g mol}^{-1}$.

32. Correct order of packing efficiency is:

• (a) fcc < bcc < simple cubic
• (b) fcc > bcc > simple cubic
• (c) fcc < bcc > simple cubic
• (d) bcc < fcc > simple cubic

Correct Answer: (b)

Explanation: Packing efficiencies are: fcc (74%), bcc (68%), and simple cubic (54%).

33. In the cubic close packing, the unit cell has:

• (a) 4 tetrahedral voids shared by 4 cells
• (b) 4 tetrahedral voids within the cell
• (c) 8 tetrahedral voids shared by 4 cells
• (d) 8 tetrahedral voids within the unit cells.

Correct Answer: (d)

Explanation: A unit cell of a ccp solid contains exactly 8 tetrahedral voids, which are all entirely within the cell.

34. Edge lengths for fcc, bcc and simple cubic respectively are:

• (a) $2\sqrt{2}r, \frac{4r}{\sqrt{3}}, 2r$
• (b) $\frac{4r}{\sqrt{3}}, 2\sqrt{2}r, 2r$
• (c) $2r, 2\sqrt{2}r, \frac{4r}{\sqrt{3}}$
• (d) $2r, \frac{4r}{\sqrt{3}}, 2\sqrt{2}r$

Correct Answer: (a)

Explanation: These are the geometric relationships between cell edge $a$ and atomic radius $r$ for these lattices.

35. In which structure is the coordination number for both ions six?

• (a) $Na^{+}Cl^{-}$
• (b) $CaF_{2}$
• (c) $Na_{2}O$
• (d) ZnS

Correct Answer: (a)

Explanation: In the rock salt structure of NaCl, both $Na^{+}$ and $Cl^{-}$ ions are octahedrally coordinated by six oppositely charged ions.

36. Mixed oxide: lattice of oxide ions. 1/5 of tetrahedral voids filled by $X^{2+}$, 1/2 of octahedral by $Y^{3+}$. Formula is:

• (a) $XY_{2}O_{4}$
• (b) $X_{2}YO_{4}$
• (c) $X_{4}Y_{5}O_{10}$
• (d) $X_{5}Y_{4}O_{10}$

Correct Answer: (c)

Explanation: Calculation based on void filling ratios ($2 \times 1/5$ for X and $1 \times 1/2$ for Y per Oxide ion) leads to $X_{2/5}Y_{1/2}O_{1}$ or $X_4Y_5O_{10}$.

37. AB rock salt, Formula wt 6.023y g, distance A-B is $y^{1/3}$ nm. Theoretical density ($in \text{ kg m}^{-3}$) is:

• (a) 1.3
• (b) 2.13
• (c) 3.01
• (d) 5.0

Correct Answer: (d)

Explanation: Using the theoretical parameters provided, calculation yields a density of 5.0 $\text{kg m}^{-3}$.

38. The total number of tetrahedral voids in the face centred unit cell is:

• (a) 6
• (b) 8
• (c) 10
• (d) 12

Correct Answer: (b)

Explanation: In an fcc (ccp) unit cell, there are two tetrahedral voids for every atom in the lattice. Since $Z=4$, there are 8 tetrahedral voids.

39. Which kind of defect is introduced by doping?

• (a) Dislocation defect
• (b) Schottky defect
• (c) Frenkel defect
• (d) Electronic defect

Correct Answer: (d)

Explanation: Doping semiconductors (like Si with B or P) introduces electronic defects by creating extra electrons or holes.

40. Which of the following conditions favours the existence of a substance in the solid state?

• (a) High temperature
• (b) Low temperature
• (c) High thermal energy
• (d) Weak cohesive forces

Correct Answer: (b)

Explanation: Low temperature reduces thermal motion, allowing intermolecular cohesive forces to hold molecules in fixed positions.

41. AB bcc, edge 387 pm. Distance between oppositely charged ions is:

• (a) 250 pm
• (b) 200 pm
• (c) 300 pm
• (d) 335 pm

Correct Answer: (d)

Explanation: In bcc, the ions touch along the body diagonal. The distance is $2r = \sqrt{3}a/2$. Calculation: $\sqrt{3} \times 387 / 2 \approx 335$ pm.

42. A tetrahedral void in a crystal implies that:

• (a) shape of the void is tetrahedral
• (b) molecules forming the void are tetrahedral
• (c) the void is surrounded tetrahedrally by four spheres
• (d) the void is surrounded by six spheres.

Correct Answer: (c)

Explanation: A tetrahedral void is the small space left when four spheres are packed together tetrahedrally.

43. Which of the following does not show ferrimagnetism?

• (a) $MgFe_{2}O_{4}$
• (b) MnO
• (c) $Fe_{3}O_{4}$
• (d) $ZnFe_{2}O_{4}$

Correct Answer: (b)

Explanation: MnO is antiferromagnetic, not ferrimagnetic.

44. The unit cell with dimensions $\alpha = \beta = \gamma = 90^{\circ}$ and $a = b \neq c$ is:

• (a) cubic
• (b) triclinic
• (c) hexagonal
• (d) tetragonal.

Correct Answer: (d)

Explanation: These parameters define the tetragonal crystal system.

45. Metal oxide $M_{0.98}O$. Fraction of the metal as $M^{3+}$ would be:

• (a) 5.08%
• (b) 7.01%
• (c) 4.08%
• (d) 6.05%

Correct Answer: (c)

Explanation: Calculation based on charge neutrality ($3x + 2(0.98 - x) = 2$) results in $x = 0.04$, which is 4.08% of the total metal.