Crystal Structures MCQ Quiz in मल्याळम - Objective Question with Answer for Crystal Structures - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക
Last updated on Mar 13, 2025
Latest Crystal Structures MCQ Objective Questions
Top Crystal Structures MCQ Objective Questions
Crystal Structures Question 1:
What is the diameter of the largest sphere in terms of lattice parameter α, which will fit the void at the center of the cube edge of a BCC crystal?
Answer (Detailed Solution Below)
Crystal Structures Question 1 Detailed Solution
Explanation:
The void formed at the center is octahedral in shape. The largest radius that can be fit in it-
\(R = \frac{\alpha }{2} - r\)
For BCC crystal structure \(\alpha = \frac{{4\;r}}{{\sqrt 3 }}\)
r is the radius of the corner atoms, α is the cube edge
\(R = \frac{\alpha }{2} - \frac{{\sqrt 3 }}{4}\alpha = 0.067\)
∴ D = 2 × R = 2 × 0.067
∴ D = 0.134 α
Crystal Structures Question 2:
Which of the following determines the frequency of atomic vibrations in the crystal
Answer (Detailed Solution Below)
Crystal Structures Question 2 Detailed Solution
- Temperature can influence the magnetic characteristics of materials.
- The rise in the temperature of solid increases the magnitude of the thermal vibrations of atoms.
- The atomic magnetic moments are free to rotate; hence, with rising temperature, the increased thermal motion of the atoms tends to randomize the directions of any moments that may be aligned.
Crystal Structures Question 3:
What is the atomic packing factor for BCC and FCC, respectively?
Answer (Detailed Solution Below)
Crystal Structures Question 3 Detailed Solution
Explanation:
The atomic packing factor is defined as the ratio of the volume occupied by the average number of atoms in a unit cell to the volume of the unit cell.
Mathematically, Atomic Packing Factor (APF):
APF \( = \frac{{{N_{atoms}} ~\times ~{V_{atoms}}}}{{{V_{unit\;cell}}}}\) ...(1)
Characteristics of various types of structures are shown in the table below:
Characteristics |
BCC |
FCC |
HCP |
---|---|---|---|
a to r relation |
\(a = \frac{{4r}}{{√ 3 }}\) |
\(a = 2√ 2 r\) |
\(a = 2r\) |
The average number of atoms |
2 |
4 |
6 |
Co-ordination number |
8 |
12 |
12 |
APF |
0.68 |
0.74 |
0.74 |
Examples |
Na, K, V, Mo, Ta, W |
Ca, Ni, Cu, Ag, Pt, Au, Pb, Al |
Be, Mg, Zn, Cd, Te |
For Cubic Unit Cell
Nav = \(N_c\over 8\) + \(N_f\over 2\) + \(N_i \over 1\)
Nav = Average no of atoms in unit cell, Nc = No of corner atoms, Ni = No of interior atoms, Nf = No of face centre atoms
Calculation:
No of atoms in f.c.c unit cell = 4
\(APF = \frac{{{N_{atoms}}{V_{atom}}}}{{{V_{crystal}}}} = \frac{{4\left( {\frac{4}{3}} \right)\pi {r^3}}}{{{{\left( {a } \right)}^3}}}= \frac{{4\left( {\frac{4}{3}} \right)\pi {r^3}}}{{{{\left( {{{2√2r}}{}} \right)}^3}}}\)
for FCC a = 2√2 r where a is side of the cube and r is atomic radius.
APF = 0.74
For BCC:
Nav = \(8\over 8\) + 0 + \(1\over 1\) = 2
√3a = 4r
Put all values in equation 1
(APF)BCC = 0.68
Crystal Structures Question 4:
When a pair of one cation and one anion are absent from ionic crystal, the resulting defect in solid is called:
Answer (Detailed Solution Below)
Crystal Structures Question 4 Detailed Solution
Explanation:
Imperfections in crystal structure involving either a single atom or a few numbers of atoms are called as point imperfections/defects.
Types of point defects or imperfections are:
- Vacancy defects
- Interstitial Defects
- Substitutional defects
- Schottky defects
- Frenkel defects
The difference between Schottky and Frenkel is explained with the help of the following diagram:
Schottky Defect |
Frenkel Defect |
Forms when oppositely charged ions leave their lattice sites, creating vacancies |
Smaller ion (usually the cation) is displaced from its lattice position to an interstitial site |
These vacancies are formed in stoichiometric units, to maintain an overall neutral charge in the ion solid |
Creates a vacancy defect at its original site and an interstitial defect at its new location |
The density of the solid crystal is less than normal |
Does not change the density of the solid |
Occurs only when there is a small difference in size between cations and anions |
Shown in ionic solids with the large size difference between the anion and cation |
Additional Information
Interstitial impurity:
- 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.
Crystal Structures Question 5:
The crystal structure of α-iron is -
Answer (Detailed Solution Below)
Crystal Structures Question 5 Detailed Solution
Concept:
Crystal structure of Material is classified as follows:
BCC: BCC stands for Body-Centered Cubic. In one unit cell, there is one atom at center, 1 atom at each corner. The crystal structure is used for Brittle materials only.
E.g. V, Mo, Ta, W, Ferrite or α-iron, δ-ferrite or δ-iron
FCC: FCC stands for Face Centered Cubic. In one unit cell, there is one atom at center, 1 atom at each corner, and 1 atom on each face. The crystal structure is used for Ductile materials only.
E.g. Ni, Cu, Ag, Pt, Au, Pb, Al, Austenite or γ-iron
The iron-carbon diagram shows the different crystal structures for different phases.
Crystal Structures Question 6:
The unit cell of a certain type of crystal is defined by three vectors a, b and c and the angle between a and b is α, b and c is β and a and c is γ. Now if α = β = γ = 90° and a = b ≠ c. The crystal structure is
Answer (Detailed Solution Below)
Crystal Structures Question 6 Detailed Solution
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.
There are 7 types of crystal systems:
Crystal System |
Angles between Axis |
Unit Cell Dimensions |
Cubic |
α = β = γ = 90° |
a = b = c |
Tetragonal |
α = β = γ = 90° |
a = b ≠ c |
Orthorhombic |
α = β = γ = 90° |
a ≠ b ≠ c |
Rhombohedral |
α = β = γ ≠ 90° |
a = b = c |
Hexagonal |
α = β = 90°, γ = 120° |
a = b ≠ c |
Monoclinic |
α = γ = 90°, β ≠ 90° |
a ≠ b ≠ c |
Triclinic |
α ≠ β ≠ γ |
a ≠ b ≠ c |
Crystal Structures Question 7:
Molybdenum has a Body-Cantered Cubic (BCC) structure with an atomic radius of 1.36 Ȧ .Then the lattice parameter for BCC molybdenum is
Answer (Detailed Solution Below)
Crystal Structures Question 7 Detailed Solution
Concept:
Body-centered cubic (BCC) structure):
In ΔABC:
(BC)2 = (AB)2 + (AC)2
\({\left( {4r} \right)^2} = {\left( {\sqrt 2 a} \right)^2} + {\left( a \right)^2}\)
(4r)2 = 3a2
\(4r = \sqrt 3 \;a\)
\(\therefore r = \frac{{\sqrt 3 }}{4}a\)
Where, lattice parameters of BCC are:
r = atomic radius
a = edge length of the unit cell
Calculation:
Given that, r = 1.36 A°
\(\because r = \frac{{\sqrt 3 }}{4}a\)
\(\therefore a = \frac{{4r}}{{\sqrt 3 }} = \frac{{4 \times 1.36}}{{1.732}} = 3.14\;A^\circ \)
Important points:
Structure |
Atomic Radius |
Simple cubic |
\(r = \frac{a}{2}\) |
BCC |
\(r = \frac{{\sqrt 3 }}{4}a\) |
FCC |
\(r = \frac{{\sqrt 2 a}}{4}\) |
Diamond cubic |
\(r = \frac{{\sqrt 3 \;a}}{8}\) |
Crystal Structures Question 8:
At room temperature, sodium crystallizes in a body-centered cubic lattice with edge length a = 4.24 Å. The theoretical density of sodium (At. wt. of Na = 23) is
Answer (Detailed Solution Below)
Crystal Structures Question 8 Detailed Solution
Formula Used:
Diagram |
|
|
|
Effective no. of lattice points (n) |
\(\Rightarrow \frac{1}{8} × 8 = 1\) |
\(\frac{1}{8} × 8 + 1 = 2\) |
\(\frac{1}{8} × 8 + \frac{1}{2} × 6 = 4\) |
Density = \(\frac{n× W}{Av.No × a^3}\)
Here, W is the atomic weight
Av. No is avogadro's number = 6.023 × 1023
n is Effective no. of lattice points
Application:
We have,
n = 2 (For BCC)
W = 23 (for Na)
a = 4.24 Å = 4.24 × 10-8 cm
Hence,
Density = \(\frac{2\times 23}{6.023\times 10^{-23}\times (4.24\times 10^{-8} )^3}\) = 1.002 g cm–3
Crystal Structures Question 9:
A unit cell of Face centred cubical crystal structure has _______ atoms per unit cell.
Answer (Detailed Solution Below)
Crystal Structures Question 9 Detailed Solution
Explanation:
An FCC structure contains atom at:
- All the eight-corner position
- All the centre position of six sides.
Characteristics |
BCC |
FCC |
HCP |
a to r relation |
\(a = \frac{{4r}}{{\sqrt 3 }}\) |
\(a = 2\sqrt 2 r\) |
\(a = 2r\) |
The average number of atoms |
2 |
4 |
6 |
Co-ordination number |
8 |
12 |
12 |
APF |
0.68 |
0.74 |
0.74 |
Examples |
Na, K, V, Mo, Ta, W |
Ca, Ni, Cu, Ag, Pt, Au, Pb, Al |
Be, Mg, Zn, Cd, Te |
Crystal Structures Question 10:
In a crystal lattice, the vacancies created in the absence of certain atoms are known as _______.
Answer (Detailed Solution Below)
Crystal Structures Question 10 Detailed Solution
Schottky defect:
- This kind of vacancy defect is found in Ionic Solids. But in ionic compounds, we need to balance the electrical neutrality of the compound so an equal number of anions and cations will be missing from the compound.
- It reduces the density of the substance.
- In this, the size of cations and anions are almost the same.
Frenkel defect:
- In ionic solids generally, the smaller ion (cation) moves out of its place and occupies an intermolecular space.
- In this case, a vacancy defect is created in its original position and the interstitial defect is experienced at its new position.
- The density of a substance remains unchanged.
- It happens when there is a huge difference in the size of anions and cations