Solid State MCQ Quiz - Objective Question with Answer for Solid State - Download Free PDF

CONCEPT:

Unit Cell Geometry and Properties

• SC (Simple Cubic)
  • Atomic radius = a / 2
  • Z (atoms per unit cell) = 1
  • Coordination number = 6
  • Packing efficiency = 52%
• BCC (Body-Centered Cubic)
  • Atomic radius = (√3 / 4) × a
  • Z = 2
  • Coordination number = 8
  • Packing efficiency = 68%
• FCC (Face-Centered Cubic)
  • Atomic radius = (√2 / 4) × a = a / (2√2)
  • Z = 4
  • Coordination number = 12
  • Packing efficiency = 74%

EXPLANATION:

• Column I to Column II Matching:
  • A. SC → Atomic radius = a / 2, Z = 1 → Match: 1
  • B. BCC → Coordination number = 8, Packing efficiency = 68% → Match: 2
  • C. FCC → Atomic radius = a / (2√2), Z = 4 → Match: 4

Correct Matching: A–1, B–2, C–4

Explanation:

The number of atoms in the unit cell (Z) is given by:\( Z = \frac{d \cdot \text{a}^3 \cdot \text{N}_A}{M}\)

Calculation:

• Given Data,
  • Molar mass (M) = 190 g/mol
  • Density (d) = \(20 g/cm^3\)
  • \(\text{a}^3 \cdot N_A = 38 \, \text{cm}^3 \cdot \,\text{mol}^{-1}\)
  • \(\text{N}_A = Avogadro's number = 6.022 \times 10^{23} \, \text{mol}^{-1}\)
• Substitute the given values into the formula:

\(Z = \frac{20 \, \text{g/cm}^3 \cdot 38 \, \text{cm}^3/\text{mol}^{-1}}{190 \, \text{g/mol}} Z = \frac{760 \, \text{g/mol}}{190 \, \text{g/mol}} Z = 4\)

Conclusion:

The number of atoms present in the unit cell is: 4

Explanation:

• Given:
  • Edge length of the fcc unit cell (a) = 393 pm
  • In a face-centered cubic (fcc) unit cell, the relation between the edge length (a) and the atomic radius (r) is given by:
• Solving for the atomic radius (r):

Conclusion:

Therefore, the radius of the atom in the fcc unit cell with an edge length of 393 pm is 138.93 pm..

CONCEPT:

Number of Atoms in Unit Cells

• A body-centered cubic (BCC) unit cell has atoms at each of the eight corners of a cube and one atom at the center of the cube.
• A face-centered cubic (FCC) unit cell has atoms at each of the eight corners of a cube and one atom at the center of each of the six faces of the cube.

EXPLANATION:

• For a body-centered cubic (BCC) unit cell:
  • The eight corner atoms contribute 1/8th of an atom each to the unit cell, so 8 * (1/8) = 1 atom from corners.
  • The single atom at the center contributes 1 atom.
  • Total number of atoms in a BCC unit cell = 1 (from corners) + 1 (from center) = 2 atoms.
• For a face-centered cubic (FCC) unit cell:
  • The eight corner atoms contribute 1/8th of an atom each to the unit cell, so 8 * (1/8) = 1 atom from corners.
  • The six face atoms contribute 1/2 of an atom each to the unit cell, so 6 * (1/2) = 3 atoms from faces.
  • Total number of atoms in an FCC unit cell = 1 (from corners) + 3 (from faces) = 4 atoms.

Therefore, the number of atoms in body-centered and face-centered cubic unit cells are 2 and 4 respectively.

CONCEPT:

Frenkel Defects

• Frenkel defects occur when an ion in a crystal lattice is displaced from its normal site to an interstitial site, leaving a vacancy at its original position.
• These defects are common in ionic crystals where there is a significant size difference between the cations and anions.
• Frenkel defects do not change the overall density of the crystal.

EXPLANATION:

The question provides several compounds. We need to analyze each one to see if they can exhibit a Frenkel defect:

• - AgCl (Silver Chloride) - This compound has a significant size difference between Ag⁺ and Cl⁻ ions, making it a candidate for Frenkel defect.
• - NaCl (Sodium Chloride) - Na⁺ and Cl⁻ ions are of similar size, so it does not exhibit a Frenkel defect.
• - Graphite - Graphite is a covalent network solid and does not have cations and anions; hence, it cannot exhibit a Frenkel defect.
• - AgBr (Silver Bromide) - Similar to AgCl, AgBr has a significant size difference between Ag⁺ and Br⁻ ions, making it another candidate for Frenkel defect.
• Therefore, the correct answer is option 2) Silver bromide.

Therefore, Silver bromide (AgBr) exhibits Frenkel defects.

Explanation:

If the atoms or atom groups in the solid are represented by points and the points are connected, the resulting lattice will consist of an orderly stacking of blocks or unit cells.

• The orthorhombic unit cell is distinguished by three lines called axes of twofold symmetry about which the cell can be rotated by 180° without changing its appearance.
• This characteristic requires that the angles between any two edges of the unit cell be right angles but the edges may be any length.

Important Points

There are 7 types of crystal systems:

Concept:

• The body-centered cubic unit cell has atoms at each of the eight corners of a cube plus one atom in the center of the cube.
• Each of the corner atoms is the corner of another cube so the corner atoms are shared among eight unit cells.

Calculation:

For body-centered cubic bcc structure,

Radius, (R) = (a×√3)/4    or a×√3 = 4×R  --- (1)

Where, a = edge length.

According to the question, the structure of a cubic unit cell can be shown as follows:

∴ a = 2(R + r)

On substituting the value of R from Eq. (1) and Eq (2), we get

\(\frac{a}{2}=\frac{√{3}}{4}a+r\)

\(r=\frac{a}{2}=\frac{√{3}}{4}a=2a-\frac{√{3a}}{4}\)

\(r=\frac{a\left( 2-√{3} \right)}{4}\)

Explanation:

Van Der Waals Crystal / Molecular Crystal.

• A solid that consists of a lattice array of molecules such as hydrogen, methane, or more organic compounds bound by Van Der Waals forces or hydrogen bonds are known as Van Der Waals Crystal.
• The general properties of the Van der Waals crystal are soft, low melting point, and a poor conductor of heat and electricity. 

Ionic crystals.

• Lattice points which occupied by charged particles (ions) and are held together by columbic forces. 
• Size and the relative number of each ion determine the crystal structure. 

Covalent Crystals. 

• Lattice points are occupied by neutral atoms. In which atoms are held together by covalent bonds. 
• These crystals are hard solids and poor conductors of electricity. 
• Covalent Solids are solids in which the constituent particles are atoms and interparticle forces are strong covalent bonds.
  Examples - Diamond, Quartz, SiO2.

EXPLANATION: From the above concept, it is clear that a diamond is a Covalent Crystal.

Concept:

The distance between the centers of two nearest tetrahedral voids in the lattice and also the minimum distance between two tetrahedral voids is \(\frac{a}{2}\)..

In fcc (face centered cubic), tetrahedral voids are located on the body diagonal at a distance of \(\frac{{\sqrt {3a} }}{4}\) from the corner. Together they form a smaller cube of edge length\(\frac{a}{2}\).

Therefore, distance between centres of two nearest tetrahedral voids in the lattice is also \(\frac{a}{2}\).

Face-centered cubic (fcc) refers to a crystal structure consisting of an atom at each cube corner and an atom in the center of each cube face. It is a close-packed plane in which on each face of the cube atoms are assumed to touch along face diagonals.

Concept:

Triclinic primitive unit cell has dimensions as, a ≠ b ≠ c and α ≠ β ≠ 90°.

Among the seven basic or primitive crystalline systems, the triclinic system is most unsymmetrical, the triclinic. In other cases, edge length and axial angles are given as follows:

Hexagonal: a = b ≠ c and α = β = 90°, γ = 120°

Monoclinic: a ≠ b ≠ c and α = γ = 90°, β ≠ 90°

Tetragonal: a ≠ b ≠ c and α = β = γ = 90°

• The parameters of all other crystal systems are given below:

Concept:

Stoichiometric Defects:

• The Stoichiometric defects are those in which the imperfections are such that the ratio between the cations and anions remains the same as represented by the chemical formula.
• Types of Stoichiometric defects are:-Schottky defect and Frenkel defect.

Non-Stoichiometric Defect:

• The Non- Stoichiometric defects are those in which the imperfections are such that the ratio between the cations and anions differs from the ideal chemical formula.
• Here, the balance of + and - charges are maintained either by having extra electrons or +ve charge.
• Its types include:- Metal excess (i. due to anion vacancy and ii. due to interstitial cations) and Metal Deficiency.

The classification of defects in solids is given below:

Explanation:

Metal excess defect due to anionic vacancies:

• Alkali halide like NaCl and KCl show this type of defect.
• When crystals of NaCl is heated in an atmosphere of sodium vapour, the sodium atoms are deposited on the surface of the crystal.
• The Cl^– ions diffuse to the surface of the crystal and combine with Na atoms to give NaCl.
• This happens by loss of an electron by sodium atoms to form Na⁺ ions.
• The released electrons diffuse into the crystal and occupy anionic sites.

• As a result, the crystal now has an excess of sodium.
• The anionic sites occupied by unpaired electrons are called F-centres.
• They impart a yellow colour to the crystals of NaCl.
• The colour results by excitation of these electrons when they absorb energy from the visible light falling on the crystals.
• Similarly, excess of lithium makes LiCl crystals pink and excess of potassium makes KCl crystals violet (or lilac).

Hence, NaCl crystals appear yellow due to F - centres.

Additional Information

 Schottky Defect:

• In order to maintain electrical neutrality, the number of missing cations and anions are equal.
• It decreases the density of the substance.
• The Schottky defect is shown by ionic substances in which the cation and anion are of almost similar sizes.
• For example, NaCl, KCl, CsCl and AgBr.

Frenkel Defect:

• The smaller ion (usually cation) is dislocated from its normal site to an interstitial site.
• It creates a vacancy defect at its the original site and an interstitial defect at its new location.
• Frenkel defect is also called a dislocation defect.
• It does not change the density of the solid.
• Frenkel defect is shown by the ionic substance in which there is a large difference in the size of ions.
• For example, ZnS, AgCl, AgBr and AgI due to small size of Zn²⁺ and Ag⁺ ions.

Interstitial Defect:

• When some constituent particles (atoms or molecules) occupy an interstitial site, the crystal is said to have an interstitial defect
• This defect increases the density of the substance.
• Ionic solids must always maintain electrical neutrality. 

Concept:

The total effective number of atoms in hcp unit lattice = Number of octahedral voids in hcp = 6

∴ Number of tetrahedral voids (TV) in hcp 

= 2 × Number of atoms in hcp lattice 

= 2 × 6 = 12

As the formula of the lattice is A₂B₃

Suppose, A B

\(\left( {\frac{1}{3} \times TV} \right)\) (hcp)

\(⇒ {\rm{\;}}\frac{1}{3} \times 12\) (6)

\(⇒ \frac{2}{3}\) 1

⇒ 2, 3

The correct answer is Changes abruptly from solid to liquid when heated. Key Points

• Crystalline solids have a highly ordered and repeating atomic arrangement, which gives them their characteristic geometric shapes.
• They have a precise melting point, which is the temperature at which the ordered atomic arrangement breaks down and the solid transitions to a liquid state.
• The 3-dimensional layout of a crystalline solid is highly regular and symmetrical, with atoms or molecules arranged in a repeating pattern.
• When heated, a crystalline solid undergoes an abrupt phase transition from solid to liquid, without passing through an intermediate liquid crystal phase.

Additional Information

• Crystalline solids are resistant to geometric deformation due to their highly ordered atomic arrangement.
• Crystalline solids have a precise melting point, which is a characteristic feature of their structure.
• The layout of a crystalline solid is highly regular and symmetrical, with no unevenness in the arrangement of atoms or molecules.
• The key term 'crystalline solid' refers to a type of solid material with a highly ordered atomic structure, which gives it unique physical and chemical properties.

Concept:

Atom A:

The number of atoms in octahedral void = 4 atoms

Half of the octahedral voids = \(\frac{4}{2} = 2\) atoms

Number of A atoms = 2 atoms

Atom B:

Number of atoms in CCP lattice structure = 4 atoms

Number of B atoms = 4 atoms

Atom Oxygen:

Number of atoms in all tetrahedral voids = 8

Number of oxygen atoms = 8 atoms