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Crystallography and Lattice Questions in English

Class 12 Chemistry · Solid State · Crystallography and Lattice

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Showing 50 of 120 questions in English

1
MediumMCQ
Which of the following statements is correct?
A
The ionic crystal of $AgBr$ has Schottky defect.
B
The unit cell having crystal parameters $a = b \ne c, \alpha = \beta = 90^{\circ}, \gamma = 120^{\circ}$ is hexagonal.
C
In ionic compounds having Frenkel defect,the ratio $\frac{r_+}{r_-}$ is high.
D
The coordination number of $Na^{+}$ ion in $NaCl$ is $4$.

Solution

(B) Option $(B)$ is correct. $A$ crystal system is classified as hexagonal if its unit cell parameters are $a = b \ne c$ and the axial angles are $\alpha = \beta = 90^{\circ}, \gamma = 120^{\circ}$.
Option $(A)$ is incorrect because $AgBr$ exhibits both Schottky and Frenkel defects.
Option $(C)$ is incorrect because Frenkel defect occurs in ionic compounds where the ratio $\frac{r_+}{r_-}$ is low (due to a large difference in size between the cation and anion).
Option $(D)$ is incorrect because the coordination number of $Na^{+}$ in $NaCl$ is $6$,not $4$.
2
AdvancedMCQ
Which of the following is correct regarding crystal systems?
A
Cubic$a \neq b = c$$\alpha = \beta \neq \gamma = 90^{\circ}$$Cu, KCl$
B
Monoclinic$a \neq b = c$$\alpha = \beta = \gamma = 90^{\circ}$$PbCrO_2, PbCrO_4$
C
Rhombohedral$a = b = c$$\alpha = \beta = \gamma \neq 90^{\circ}$$CaCO_3, HgS$
D
Triclinic$a = b = c$$\alpha \neq \beta \neq \gamma \neq 90^{\circ}$$K_2Cr_2O_7, CuSO_4 \cdot 5H_2O$

Solution

(C) The correct crystal system parameters are as follows:
$C$. Rhombohedral: $a = b = c$ and $\alpha = \beta = \gamma \neq 90^{\circ}$.
Examples include $CaCO_3$ (calcite) and $HgS$ (cinnabar).
Option $A$ is incorrect as Cubic is $a = b = c$ and $\alpha = \beta = \gamma = 90^{\circ}$.
Option $B$ is incorrect as Monoclinic is $a \neq b \neq c$ and $\alpha = \gamma = 90^{\circ}, \beta \neq 90^{\circ}$.
Option $D$ is incorrect as Triclinic is $a \neq b \neq c$ and $\alpha \neq \beta \neq \gamma \neq 90^{\circ}$.
3
MediumMCQ
Tetragonal crystal system has the following unit cell dimensions:
A
$a = b = c$ and $\alpha = \beta = \gamma = 90^\circ$
B
$a = b \ne c$ and $\alpha = \beta = \gamma = 90^\circ$
C
$a \ne b \ne c$ and $\alpha = \beta = \gamma = 90^\circ$
D
$a = b \ne c$ and $\alpha = \beta = 90^\circ, \gamma = 120^\circ$

Solution

(B) The tetragonal crystal system is characterized by the unit cell dimensions $a = b \ne c$ and the interfacial angles $\alpha = \beta = \gamma = 90^\circ$. Therefore,option $B$ is correct.
4
MediumMCQ
How many space lattices are obtainable from the different crystal systems?
A
$7$
B
$14$
C
$32$
D
$230$

Solution

(B) There are $7$ crystal systems in total.
These $7$ crystal systems give rise to $14$ possible Bravais lattices (space lattices).
5
MediumMCQ
Example of a unit cell with crystallographic dimensions $a \neq b \neq c, \alpha = \gamma = 90^{\circ}, \beta \neq 90^{\circ}$ is:
A
Calcite
B
Graphite
C
Rhombic sulphur
D
Monoclinic sulphur

Solution

(D) The given crystallographic dimensions $a \neq b \neq c$ and $\alpha = \gamma = 90^{\circ}, \beta \neq 90^{\circ}$ correspond to the Monoclinic crystal system.
Monoclinic sulphur is a classic example of this crystal system.
6
MediumMCQ
What type of lattice is found in potassium chloride crystal?
A
Face-centred cubic
B
Body-centred cubic
C
Simple cubic
D
Simple tetragonal

Solution

(A) Potassium chloride $(KCl)$ crystallizes in a face-centred cubic $(fcc)$ lattice structure,similar to sodium chloride $(NaCl)$.
In this structure,both $K^+$ and $Cl^-$ ions occupy positions in an $fcc$ arrangement.
7
MediumMCQ
The three-dimensional graph of lattice points which sets the pattern for the whole lattice is called:
A
Space lattice
B
Simple lattice
C
Unit cell
D
Crystal lattice

Solution

(C) The smallest repeating structural unit of a crystal lattice that,when repeated in three dimensions,generates the entire crystal structure is known as the $ \text{unit cell} $.
Therefore,the correct option is $ (C) $.
8
EasyMCQ
Crystals can be classified into how many basic crystal systems?
A
$3$
B
$14$
C
$7$
D
$4$

Solution

(C) Crystals are classified into $7$ basic crystal systems based on the parameters of their unit cells (axial lengths $a, b, c$ and axial angles $\alpha, \beta, \gamma$). These are: Cubic,Tetragonal,Orthorhombic,Hexagonal,Rhombohedral,Monoclinic,and Triclinic.
9
MediumMCQ
The total number of Bravais lattice arrangements in different crystal systems is
A
$3$
B
$7$
C
$8$
D
$14$

Solution

(D) The total number of Bravais lattice arrangements in different crystal systems is $14$.
These $14$ Bravais lattices are derived from the $7$ basic crystal systems: Cubic,Tetragonal,Orthorhombic,Monoclinic,Hexagonal,Rhombohedral,and Triclinic.
10
MediumMCQ
Which of the following dimensions represents a monoclinic crystal system?
A
$a \neq b \neq c, \alpha = \gamma = 90^\circ, \beta \neq 90^\circ$
B
$a = b = c, \alpha = \beta = \gamma = 90^\circ$
C
$a = b \neq c, \alpha = \beta = \gamma = 90^\circ$
D
$a \neq b \neq c, \alpha \neq \beta \neq \gamma \neq 90^\circ$

Solution

(A) The monoclinic crystal system is characterized by the following dimensions:
$a \neq b \neq c$
$\alpha = \gamma = 90^\circ$
$\beta \neq 90^\circ$
Therefore,the correct option is $(A)$.
11
EasyMCQ
Bravais lattices are of (in $types$)
A
$8$
B
$12$
C
$14$
D
$9$

Solution

(C) There are $14$ types of Bravais lattices (space lattices) possible in a crystal system,which are categorized based on the seven crystal systems.
12
DifficultMCQ
The crystal system of a compound with unit cell dimensions $a = 0.387 \ nm$,$b = 0.387 \ nm$ and $c = 0.504 \ nm$ and $\alpha = \beta = 90^{\circ}$ and $\gamma = 120^{\circ}$ is:
A
Cubic
B
Hexagonal
C
Orthorhombic
D
Rhombohedral

Solution

(B) The crystal system is determined by the unit cell parameters $a, b, c$ and the interfacial angles $\alpha, \beta, \gamma$.
Given parameters are $a = b = 0.387 \ nm$,$c = 0.504 \ nm$,which implies $a = b \neq c$.
The angles are $\alpha = \beta = 90^{\circ}$ and $\gamma = 120^{\circ}$.
These specific conditions ($a = b \neq c$ and $\alpha = \beta = 90^{\circ}, \gamma = 120^{\circ}$) correspond to the Hexagonal crystal system.
13
MediumMCQ
$A$ metal has $bcc$ structure and the edge length of its unit cell is $3.04 \, \mathring{A}$. The volume of the unit cell in $cm^3$ will be
A
$1.6 \times 10^{21} \, cm^3$
B
$2.81 \times 10^{-23} \, cm^3$
C
$6.02 \times 10^{-23} \, cm^3$
D
$6.6 \times 10^{-24} \, cm^3$

Solution

(B) The volume of a cubic unit cell is given by the formula $V = a^3$,where $a$ is the edge length.
Given $a = 3.04 \, \mathring{A} = 3.04 \times 10^{-8} \, cm$.
Therefore,$V = (3.04 \times 10^{-8} \, cm)^3$.
$V = 28.11 \times 10^{-24} \, cm^3 = 2.81 \times 10^{-23} \, cm^3$.
14
MediumMCQ
In a face-centred cubic $(FCC)$ unit cell,the edge length $(a)$ in terms of atomic radius $(r)$ is:
A
$\frac{4}{\sqrt{3}} r$
B
$\frac{4}{\sqrt{2}} r$
C
$2r$
D
$\frac{\sqrt{3}}{2} r$

Solution

(B) In a face-centred cubic $(FCC)$ unit cell,the atoms touch along the face diagonal.
The length of the face diagonal is $\sqrt{2} a$,where $a$ is the edge length.
Since the face diagonal consists of four atomic radii $(r + 2r + r = 4r)$,we have the relation: $4r = \sqrt{2} a$.
Rearranging for the edge length $a$,we get: $a = \frac{4r}{\sqrt{2}}$.
15
MediumMCQ
Most crystals show good cleavage because their atoms,ions or molecules are
A
Weakly bonded together
B
Strongly bonded together
C
Spherically symmetrical
D
Arranged in planes

Solution

(D) $ (d) $ Crystals show good cleavage because their constituent particles are arranged in planes. Cleavage is the property of a crystal to break along specific planes of weakness.
16
MediumMCQ
The number of atoms present in a unit cell of a monoatomic substance with a simple cubic lattice is:
A
$6$
B
$3$
C
$2$
D
$1$

Solution

(D) In a simple cubic lattice,atoms are present only at the corners of the cube.
Each corner atom is shared by $8$ adjacent unit cells.
Therefore,the contribution of each corner atom to a single unit cell is $\frac{1}{8}$.
Since there are $8$ corners in a cube,the total number of atoms $(z)$ per unit cell is:
$z = 8 \times \frac{1}{8} = 1$.
Thus,the correct option is $D$.
17
EasyMCQ
$A$ match box exhibits
A
Cubic geometry
B
Monoclinic geometry
C
Orthorhombic geometry
D
Tetragonal geometry

Solution

(C) . Orthorhombic geometry has $a \neq b \neq c$ and $\alpha = \beta = \gamma = 90^{\circ}$. The shape of a match box obeys this geometry.
18
MediumMCQ
Which crystal system has no axis of rotation of symmetry?
A
Hexagonal
B
Orthorhombic
C
Cubic
D
Triclinic

Solution

(D) The triclinic crystal system is the least symmetric crystal system. It possesses no axis of rotation of symmetry and no plane of symmetry. It only has a center of symmetry.
19
MediumMCQ
$FeSO_4 \cdot 7H_2O$ shows isomorphism with
A
$ZnSO_4 \cdot 7H_2O$
B
$MnSO_4 \cdot 4H_2O$
C
$CaSO_4 \cdot 5H_2O$
D
$CaCl_2 \cdot 2H_2O$

Solution

(A) Isomorphic compounds are those that crystallize in the same structure and have similar chemical formulas.
$FeSO_4 \cdot 7H_2O$ (ferrous sulfate heptahydrate) and $ZnSO_4 \cdot 7H_2O$ (zinc sulfate heptahydrate) both crystallize in the same orthorhombic system,making them isomorphous.
20
MediumMCQ
Heat treatment alters the properties of steel due to:
A
Chemical reaction on heating
B
Partial rusting
C
Change in the residual energy
D
Change in the lattice structure due to differential rate of cooling

Solution

(D) Heat treatment involves heating steel to a specific temperature and then cooling it at a controlled rate.
This process changes the arrangement of atoms in the crystal lattice (e.g.,from austenite to martensite or pearlite),which significantly alters the mechanical properties of the steel such as hardness,ductility,and strength.
Therefore,the correct option is $D$.
21
EasyMCQ
When atoms are placed at the corners of all $12$ edges of a unit cell,what is the number of atoms present per unit cell?
A
$1$
B
$2$
C
$3$
D
$4$

Solution

(A) cube has $8$ corners. Each corner atom is shared by $8$ adjacent unit cells.
Therefore,the contribution of each corner atom to the unit cell is $\frac{1}{8}$.
Total number of atoms per unit cell = $8 \times \frac{1}{8} = 1$.
This represents a primitive unit cell.
22
EasyMCQ
Which of the following unit cell parameters represents the tetragonal crystal system?
A
$a = b = c, \alpha = \beta = \gamma = 90^\circ$
B
$a = b \neq c, \alpha = \beta = \gamma = 90^\circ$
C
$a \neq b \neq c, \alpha = \beta = \gamma = 90^\circ$
D
$a = b \neq c, \alpha = \beta = 90^\circ, \gamma = 120^\circ$

Solution

(B) The tetragonal crystal system is characterized by the unit cell parameters $a = b \neq c$ and axial angles $\alpha = \beta = \gamma = 90^\circ$.
Option $A$ represents the cubic system.
Option $B$ represents the tetragonal system.
Option $C$ represents the orthorhombic system.
Option $D$ represents the hexagonal system.
23
MediumMCQ
Select the correct option using $T$ (True) or $F$ (False) for the following statements regarding crystal systems:
$(1)$ Crystal system: Cubic,Axial distance: $a = b = c$,Axial angle: $\alpha = \beta = \gamma = 90^{\circ}$,Example: $Cu, KCl$
$(2)$ Crystal system: Monoclinic,Axial distance: $a \neq b \neq c$,Axial angle: $\alpha = \gamma = 90^{\circ}, \beta \neq 90^{\circ}$,Example: $PbCrO_4$
$(3)$ Crystal system: Trigonal (Rhombohedral),Axial distance: $a = b = c$,Axial angle: $\alpha = \beta = \gamma \neq 90^{\circ}$,Example: $CaCO_3, HgS$
$(4)$ Crystal system: Triclinic,Axial distance: $a \neq b \neq c$,Axial angle: $\alpha \neq \beta \neq \gamma \neq 90^{\circ}$,Example: $K_2Cr_2O_7, CuSO_4 \cdot 5H_2O$
A
$TTFT$
B
$FFFF$
C
$TFFT$
D
$FTTF$
24
EasyMCQ
How many types of Bravais lattices are there?
A
$10$
B
$8$
C
$7$
D
$14$

Solution

(D) The $14$ Bravais lattices are the distinct spatial arrangements of points in a crystal lattice. These are derived from the $7$ primitive crystal systems by considering different types of centering (primitive,body-centered,face-centered,and end-centered).
25
MediumMCQ
$A$ metal has a $bcc$ structure. If the edge length of its unit cell is $3.04 \ \overset{\circ}{A}$,what is the volume of the unit cell in $cm^3$?
A
$1.6 \times 10^{-21} \ cm^3$
B
$2.81 \times 10^{-23} \ cm^3$
C
$6.02 \times 10^{-23} \ cm^3$
D
$6.6 \times 10^{-24} \ cm^3$

Solution

(B) The volume of a unit cell is given by the formula $V = a^3$.
Given edge length $a = 3.04 \ \overset{\circ}{A} = 3.04 \times 10^{-8} \ cm$.
Therefore,$V = (3.04 \times 10^{-8} \ cm)^3$.
$V = 28.11 \times 10^{-24} \ cm^3 = 2.81 \times 10^{-23} \ cm^3$.
26
EasyMCQ
The crystal system following the parameters $a \neq b \neq c$ and $\alpha \neq \beta \neq \gamma \neq 90^\circ$ is ...... .
A
Triclinic system
B
Orthorhombic system
C
Monoclinic system
D
Tetragonal system

Solution

(A) The crystal system defined by the parameters $a \neq b \neq c$ and $\alpha \neq \beta \neq \gamma \neq 90^\circ$ is the Triclinic system.
This is the most unsymmetrical crystal system among the seven primitive crystal systems.
27
EasyMCQ
The parameters of a monoclinic crystal system are .......
A
$a \neq b \neq c$ and $\alpha = \gamma = 90^\circ, \beta \neq 90^\circ$
B
$a = b = c$ and $\alpha = \beta = \gamma = 90^\circ$
C
$a = b \neq c$ and $\alpha = \beta = \gamma = 90^\circ$
D
$a \neq b \neq c$ and $\alpha \neq \beta \neq \gamma \neq 90^\circ$

Solution

(A) In a monoclinic crystal system,the axial lengths are unequal $(a \neq b \neq c)$.
Regarding the axial angles,two angles are equal to $90^\circ$ $(\alpha = \gamma = 90^\circ)$,while the third angle $(\beta)$ is not equal to $90^\circ$ $(\beta \neq 90^\circ)$.
28
EasyMCQ
Which of the following represents the correct axial distances and axial angles for the rhombohedral crystal system?
A
$a = b = c, \alpha = \beta = \gamma \neq 90^\circ$
B
$a = b \neq c, \alpha = \beta = 90^\circ, \gamma = 120^\circ$
C
$a \neq b \neq c, \alpha = \gamma = 90^\circ \neq \beta$
D
$a \neq b \neq c, \alpha \neq \beta \neq \gamma \neq 90^\circ$

Solution

(A) The rhombohedral (or trigonal) crystal system is characterized by the following parameters:
$1$. Axial distances: $a = b = c$
$2$. Axial angles: $\alpha = \beta = \gamma \neq 90^\circ$
Therefore,the correct option is $A$.
29
EasyMCQ
For an orthorhombic crystal system,the axial lengths are $a \neq b \neq c$. What are the axial angles?
A
$\alpha = \beta = \gamma \neq 90^\circ$
B
$\alpha = \beta = \gamma = 90^\circ$
C
$\alpha = \gamma = 90^\circ, \beta = 120^\circ$
D
$\alpha \neq \beta \neq \gamma \neq 90^\circ$

Solution

(B) In an orthorhombic crystal system,the unit cell parameters are defined as follows:
$1$. Axial lengths: $a \neq b \neq c$
$2$. Axial angles: $\alpha = \beta = \gamma = 90^\circ$
Therefore,the correct option is $B$.
30
EasyMCQ
Which of the following crystal systems has $a = b = c$ and $\alpha = \beta = \gamma \neq 90^o$?
A
Tetragonal
B
Hexagonal
C
Rhombohedral
D
Monoclinic

Solution

(C) The crystal system with axial lengths $a = b = c$ and axial angles $\alpha = \beta = \gamma \neq 90^o$ is known as the Rhombohedral (or Trigonal) system.
Crystal SystemAxial DistancesAxial Angles
Tetragonal$a = b \neq c$$\alpha = \beta = \gamma = 90^o$
Hexagonal$a = b \neq c$$\alpha = \beta = 90^o, \gamma = 120^o$
Rhombohedral$a = b = c$$\alpha = \beta = \gamma \neq 90^o$
Monoclinic$a \neq b \neq c$$\alpha = \gamma = 90^o, \beta \neq 90^o$
31
MediumMCQ
Statement $1$: Graphite is an example of a tetragonal system.
Statement $2$: For a tetragonal system,$a = b \neq c$,$\alpha = \beta = 90^o$,$\gamma = 90^o$.
A
Statement $1$ and Statement $2$ are both true and Statement $2$ is the correct explanation of Statement $1$.
B
Statement $1$ and Statement $2$ are both true,but Statement $2$ is not the correct explanation of Statement $1$.
C
Statement $1$ and Statement $2$ are both false.
D
Statement $1$ is true,but Statement $2$ is false.

Solution

(C) Graphite crystallizes in a hexagonal system,not a tetragonal system. Therefore,Statement $1$ is false.
For a tetragonal system,the axial parameters are $a = b \neq c$ and the axial angles are $\alpha = \beta = \gamma = 90^o$. The parameters given in Statement $2$ ($a = b \neq c$,$\alpha = \beta = 120^o$,$\gamma = 90^o$) describe a hexagonal system. Therefore,Statement $2$ is also false.
Thus,both statements are false.
32
EasyMCQ
The parameters $a = b = c$ and $\alpha = \beta = \gamma \neq 90^\circ$ belong to which crystal system?
A
Tetragonal
B
Hexagonal
C
Rhombohedral
D
Monoclinic

Solution

(C) The crystal system with parameters $a = b = c$ and $\alpha = \beta = \gamma \neq 90^\circ$ is known as the Rhombohedral (or Trigonal) system.
In this system,all three edge lengths are equal,and all three interfacial angles are equal but not equal to $90^\circ$.
33
EasyMCQ
Which of the following crystal systems does not possess an axis of rotation?
A
Hexagonal
B
Orthorhombic
C
Cubic
D
Triclinic

Solution

(D) The $7$ crystal systems are categorized based on their symmetry elements. Among these,the $Triclinic$ system is the least symmetrical and does not possess any axis of rotation or plane of symmetry.
34
EasyMCQ
The tetragonal crystal system has which of the following unit cell parameters?
A
$a = b = c$ and $\alpha = \beta = \gamma = 90^o$
B
$a = b \neq c$ and $\alpha = \beta = \gamma = 90^o$
C
$a \neq b \neq c$ and $\alpha = \beta = \gamma = 90^o$
D
$a = b \neq c$ and $\alpha = \beta = 90^o, \gamma = 120^o$

Solution

(B) In a tetragonal crystal system,the unit cell parameters are defined by the axial lengths $a = b \neq c$ and the axial angles $\alpha = \beta = \gamma = 90^o$.
Therefore,the correct option is $B$.
35
EasyMCQ
Which crystal system does diamond possess?
A
Cubic
B
Triclinic
C
Tetragonal
D
Hexagonal

Solution

(A) Diamond has a face-centered cubic $(fcc)$ structure,which belongs to the cubic crystal system. In this structure,each carbon atom is $sp^3$ hybridized and bonded to four other carbon atoms in a tetrahedral geometry.
36
DifficultMCQ
$A$ solid compound $XY$ has $NaCl$ structure. If the radius of the cation is $100 \ pm,$ the radius of the anion $(Y^-)$ will be .............. $pm$.
A
$275.1$
B
$322.5$
C
$241.5$
D
$165.7$

Solution

(C) For a compound with $NaCl$ structure, the limiting radius ratio is $0.414$.
The radius ratio formula is given by $\frac{r^+}{r^-} = 0.414$.
Given that the radius of the cation $r^+ = 100 \ pm$, we substitute this into the equation:
$\frac{100}{r^-} = 0.414$
$r^- = \frac{100}{0.414} \approx 241.54 \ pm$.
Rounding to the nearest option, the radius of the anion is $241.5 \ pm$.
37
MediumMCQ
Select the incorrect statement.
A
$F$-centres are a factor for imparting the colour to the crystal.
B
Stoichiometry of crystal remains unaffected due to Schottky defect.
C
In orthorhombic crystal,each interfacial angle is $90^o$.
D
There are four unit cells in tetragonal crystal system.

Solution

(D) $1$. $F$-centres (Farbe centres) are anionic vacancies occupied by electrons,which impart colour to the crystal. This is a correct statement.
$2$. Schottky defect involves the loss of equal numbers of cations and anions,maintaining the electrical neutrality and stoichiometry of the crystal. This is a correct statement.
$3$. In an orthorhombic crystal system,the axial angles are $\alpha = \beta = \gamma = 90^o$. This is a correct statement.
$4$. The tetragonal crystal system consists of only two types of unit cells: primitive (simple) and body-centred. There are not four unit cells. Therefore,this statement is incorrect.
38
DifficultMCQ
Which of the following does not have a hexagonal crystal system?
A
Graphite
B
Zinc oxide
C
$CdS$
D
$HgS$

Solution

(D) The hexagonal crystal system is characterized by unit cell dimensions $a = b \neq c$ and angles $\alpha = \beta = 90^{\circ}, \gamma = 120^{\circ}$.
Graphite,Zinc oxide $(ZnO)$,and Cadmium sulfide $(CdS)$ (in its wurtzite form) crystallize in the hexagonal system.
However,Mercury$(II)$ sulfide $(HgS)$,specifically in its cinnabar form,crystallizes in the trigonal (rhombohedral) crystal system.
Therefore,$HgS$ does not have a hexagonal crystal system.
39
DifficultMCQ
Body-centred cubic and face-centred cubic unit cells have $n_1$ and $n_2$ effective number of atoms. Which one of the following $[n_1, n_2]$ combinations is correct?
A
$(4, 1)$
B
$(4, 2)$
C
$(1, 4)$
D
$(2, 4)$

Solution

(D) For a body-centred cubic $(bcc)$ unit cell,the effective number of atoms $n_1 = 2$.
For a face-centred cubic $(fcc)$ unit cell,the effective number of atoms $n_2 = 4$.
Therefore,the correct combination is $(n_1, n_2) = (2, 4)$.
40
MediumMCQ
In a tetragonal crystal :-
A
$ \alpha = \beta = 90^\circ \neq \gamma; a = b = c $
B
$ \alpha = \beta = \gamma = 90^\circ; a = b \neq c $
C
$ \alpha = \beta = \gamma = 90^\circ; a \neq b \neq c $
D
$ \alpha = \beta = 90^\circ; \gamma = 120^\circ; a = b \neq c $

Solution

(B) tetragonal crystal system is characterized by the axial lengths $a = b \neq c$ and the axial angles $\alpha = \beta = \gamma = 90^\circ$.
41
EasyMCQ
Which of the following primitive cells show the given parameters?
$a \neq b \neq c, \alpha = \beta = \gamma = 90^{\circ}$
A
Cubic
B
Tetragonal
C
Orthorhombic
D
Hexagonal

Solution

(C) In an orthorhombic crystal system,the axial lengths are unequal,i.e.,$a \neq b \neq c$,and all axial angles are equal to $90^{\circ}$,i.e.,$\alpha = \beta = \gamma = 90^{\circ}$.
Hence,Option $C$ is the correct answer.
42
EasyMCQ
$a \ne b \ne c$,$\alpha \ne \beta \ne \gamma \ne 90^{\circ}$ represent:
A
Tetragonal system
B
Orthorhombic system
C
Monoclinic system
D
Triclinic system

Solution

(D) The crystal system defined by the parameters $a \ne b \ne c$ and $\alpha \ne \beta \ne \gamma \ne 90^{\circ}$ is the triclinic system.
In this system,none of the axial lengths are equal,and none of the interfacial angles are equal to each other or to $90^{\circ}$.
Examples of substances crystallizing in the triclinic system include $K_{2}Cr_{2}O_{7}$ and $H_{3}BO_{3}$.
43
MediumMCQ
Maximum possible number of three-dimensional and two-dimensional lattices are respectively:
A
$13$ and $7$
B
$12$ and $3$
C
$11$ and $6$
D
$14$ and $5$

Solution

(D) In two dimensions,there are $5$ different Bravais lattices: square,rectangular,centered rectangular,hexagonal,and parallelogram lattices.
In three dimensions,there are $14$ Bravais lattices.
These $14$ Bravais lattices in three dimensions are derived from the $7$ crystal systems.
Therefore,the correct option is $(D)$.
44
EasyMCQ
In a monoclinic unit cell,the relation of sides and angles are respectively
A
$a \neq b \neq c$ and $\alpha = \beta = \gamma = 90^{\circ}$
B
$a \neq b \neq c$ and $\alpha = \gamma = 90^{\circ} \neq \beta$
C
$a \neq b \neq c$ and $\alpha = \gamma = 90^{\circ} \neq \beta$ (Note: Corrected to match standard definition)
D
$a \neq b \neq c$ and $\alpha \neq \beta \neq \gamma \neq 90^{\circ}$

Solution

(B) The monoclinic crystal system is one of the $7$ primitive crystal systems.
In a monoclinic unit cell,the side lengths are unequal,represented as $a \neq b \neq c$.
The angles are defined such that two angles are $90^{\circ}$ and one is not,specifically $\alpha = \gamma = 90^{\circ}$ and $\beta \neq 90^{\circ}$.
45
EasyMCQ
Which primitive unit cell has unequal edge length $(a \ne b \ne c)$ and all axial angles different from $90^{\circ}$?
A
Triclinic
B
Hexagonal
C
Monoclinic
D
Tetragonal

Solution

(A) In a Triclinic unit cell,the parameters are defined as $a \ne b \ne c$ and $\alpha \ne \beta \ne \gamma \ne 90^{\circ}$.
This represents the most unsymmetrical crystal system.
46
DifficultMCQ
Chromium metal crystallises in a body-centred cubic $(bcc)$ lattice. The edge length of the unit cell is found to be $287 \, pm$. The atomic radius of chromium will be ............. $pm$.
A
$87$
B
$62.135$
C
$124.27$
D
None of these

Solution

(C) For a $bcc$ crystal, the relationship between the atomic radius $(r)$ and the edge length $(a)$ is given by $r = \frac{\sqrt{3}}{4} a$.
Given $a = 287 \, pm$.
Substituting the value: $r = \frac{1.732}{4} \times 287$.
$r = 0.433 \times 287 = 124.27 \, pm$.
Thus, the atomic radius of chromium is $124.27 \, pm$.
Therefore, option $(C)$ is the correct answer.
47
MediumMCQ
The unit cell present in the crystal lattice of diamond is
A
Cubic
B
Tetragonal
C
Hexagonal
D
Trigonal

Solution

(A) The diamond crystal structure is based on a face-centered cubic $(FCC)$ lattice.
It consists of two interpenetrating $FCC$ sublattices,where one is displaced along the body diagonal of the cubic cell by one-fourth of the length of the diagonal.
Therefore,the fundamental unit cell of diamond is cubic.
48
MediumMCQ
Which of the following crystal systems exists only as a primitive Bravais lattice?
A
Monoclinic
B
Trigonal
C
Cubic
D
Hexagonal

Solution

(D) The $14$ Bravais lattices are distributed among the $7$ crystal systems.
Among these,the $Hexagonal$,$Trigonal$ (Rhombohedral),and $Triclinic$ systems exist only in the primitive $(P)$ form.
$Cubic$ systems exist as $Primitive$ $(P)$,$Body-centered$ $(I)$,and $Face-centered$ $(F)$.
$Monoclinic$ systems exist as $Primitive$ $(P)$ and $Base-centered$ $(C)$.
Therefore,among the given options,$Hexagonal$ is the correct choice as it only exists as a primitive lattice.
49
EasyMCQ
How many kinds of Bravais lattices are possible in crystal systems?
A
$23$
B
$7$
C
$230$
D
$14$

Solution

(D) There are $14$ kinds of space lattices possible for crystals,which are known as Bravais lattices.
50
EasyMCQ
In a tetragonal crystal system,which of the following conditions is correct?
A
$a = b \ne c, \alpha = \beta = \gamma = 90^\circ$
B
$\alpha = \beta = \gamma = 90^\circ, a = b \ne c$
C
$\alpha = \beta = \gamma = 90^\circ, a \ne b \ne c$
D
$\alpha = \beta = 90^\circ, \gamma = 120^\circ, a = b \ne c$

Solution

(B) In a tetragonal crystal system,the unit cell dimensions are defined by $a = b \ne c$ and the interfacial angles are $\alpha = \beta = \gamma = 90^\circ$.
Both options $A$ and $B$ represent the same mathematical condition. However,standard convention lists the axial lengths first followed by the angles. Therefore,option $B$ is the most standard representation.

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