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The correct option is (d) 1.13 x 10^-1 nm

The explanation: GIVEN,

RADIUS of CHLORIDE ion (r^–) = 0.154 nm

 Let radius of cation = r^+

 For Octahedral Voids, r^+ / r^– = 0.732 (for MAXIMUM value of the size of the cation)

Therefore, r^+ = 0.732 x 0.154 = 1.13 x 10^-1 nm.

Correct option is (c) triangular

Easiest explanation: Two-dimensional hexagonal close packed structure are FORMED when one ROW of a one-dimensional structure is placed below ANOTHER in such a way that spheres of second row fit in the depressions of the first row and thereby creating triangular VOIDS between them.

Right answer is (a) Six

Easiest explanation: A unit cell is characterized by six parameters i.e. the three COMMON edge LENGTHS a, b, c and three angles between the EDGES that are α, β, γ. These are referred to as inter-axial lengths and angles, respectively. The POSITION of a unit cell can be determined by fractional coordinates along the cell edges.

Right choice is (c) metallic

To EXPLAIN: Metallic bonds are formed between positive metal ions and the sea of delocalized ELECTRONS. This BOND is stronger than covalent and ionic bonds. Due to the mobility of electrons, conduction of heat and electricity is FEASIBLE.

The correct answer is (b) interstitial

To explain: STAINLESS STEEL is an interstitial alloy. Carbon atoms are introduced into interstitial spaces of iron lattice as an impurity. Further ALLOYING sees the introduction of nickel, CHROMIUM in the interstitial spaces.

Right answer is (c) POINT defect

Explanation: When there is a fault in the arrangement of a CONSTITUENT particle such as an atom, ion or MOLECULE, and the fault exists at a point in the lattice structure, it is CALLED as a point defect.

Correct option is (d) 2

The explanation is: In body-centered cubic unit CELL, ONE atom is present at each of the CORNERS and one atom at its body center.

• 8 corners × \(\FRAC{1}{8}\)th of an atom = 1

• 1 body-centered atom

Thus, the total number of atoms in body-centered cubic unit cell: 1+1=2 atoms.

Correct option is (B) \(\frac{8}{3}\)πr^3

To explain I would say: Since particles are assumed to be spheres and volume of ONE SPHERE is \(\frac{4}{3}\)πr^3, TOTAL volume of all particles in BCC = 2 x \(\frac{4}{3}\)πr^3=\(\frac{8}{3}\)πr^3 since a BCC has 2 particles per cell.

Correct answer is (b) Primitive cell

Easiest explanation: According to classification of unit CELLS, a primitive unit cell is one which has all constituent PARTICLES located at its corners. BCC has one particle PRESENT at the center including the corners. FCC has an individual cell shared between the faces of adjacent cells. END centered cells have cells present at centers of two opposite faces.

The correct answer is (d) 12

Explanation: FCC, CCP and HCP are unit cells with least free space available i.e. highest PACKING efficiency. The coordination number of GIVEN cells are 12.

Correct choice is (c) solids

Easiest explanation: In solids, the constituent PARTICLES tend to be closely packed due to STRONG forces between them. HENCE, solids are stable and have a definite SHAPE.

Right ANSWER is (d) AAA

The explanation: Simple cubic lattice results from 3D close packing from 2D square-packed layers. When ONE 2D layer is placed on top of the other, the corresponding SPHERES of the second layer are exactlyon top of the first one. Since both have the same, exact arrangement it is AAA TYPE.

Correct ANSWER is (c) covalent SOLIDS

Easy explanation: QUARTZ is a common example of covalent solids. In covalent solids, the constituent particles are attached to each other by covalent bonds. Diamond, graphite, silicon are other examples of covalent solids.

The correct option is (b) 2

To elaborate: Two-dimensional close packed STRUCTURE can be generated using the one-dimensional close packed structures. This can be done in 2 ways:

• By placing one row of one-dimensional structure below ANOTHER in such a way that the SPHERES are one below the another.

• By placing one row of one-dimensional structure below another such that spheres of second row FIT in the depressions of the first row.

The correct OPTION is (c) 8

The best EXPLANATION: Coordination number of a unit cell is defined as the number of atoms/ions that surround the central atom/ion. In the CASE of BCC, the central particle is surrounded by 8 particles hence, 8.

The correct option is (d) Hexaclinic

To explain: Hexaclinic is not a crystal system. Their crystal system are CUBIC, tetragonal, RHOMBOHEDRAL or trigonal, orthorhombic or RHOMBIC, monoclinic, TRICLINIC and HEXAGONAL.

The correct ANSWER is (C) covalent solid

To explain: The solids in which constituent particles are ATTACHED to each other by covalent bonds are called covalent solids. Diamond, graphite, silicon, SiC, AIN, quartz are EXAMPLES of covalent solids.

Correct option is (d) On heating, ferrimagnetic substanceslose ferrimagnetism

For EXPLANATION I would say: On heating, ferrimagnetic substances become PARAMAGNETIC and hence, lose their ferromagnetism. NaCl is DIAMAGNETIC in nature. Cobalt is a ferromagnetic SUBSTANCE.

Right OPTION is (d) Both, SHORT range and long range order

Best explanation: Only short range order is a FEATURE of amorphous solids. Crystalline solids exhibit both short and long range order. Crystalline solids are FORMED by repetitive arrangement of unit cells.

Right CHOICE is (c) \(\frac{1}{8}\)th

Explanation: In primitive UNIT cubic cell, each atom at the corner is SHARED between 8 adjacent unit CELLS. Thus, only \(\frac{1}{8}\)th of an atom (or ion or MOLECULE) belongs to a particular unit cell.

Correct OPTION is (d) AB

For explanation I would SAY: The description is of a BCC. For BCC, each atom at the corner is shared by 8 unit CELLS. One atom at the CENTER wholly belongs to the corresponding unit cell.

Therefore, total number of atoms of A present=\(\frac{1}{8}\) x 8=1

Total number of atoms of B present=1

Therefore, A:B=1:1 implying the formula of the COMPOUND is AB.

Correct option is (a) True

Best EXPLANATION: All big crystals have some or the other defects in the arrangement of their constituents. An ideal crystal does not exist. These defects are more if the crystallization process occurs at a FASTER rate. Hence, SLOWING down the process minimizes the defects. It is akin to starting with one crystal (unit) and adding to it from all SIDES to create a BIGGER crystal. Defects are produced due to some irregularity in this arrangement.

The CORRECT option is (c) 4.32 Å

The explanation: Given,

Radius of Chloride ion (r^–) = 0.154 nm

DISTANCE between the centres of the Chloride ions = 2 X 0.154 = 0.308 nm

Let the EDGE length of cube = a

Distance between RB^+ and Cl^– ions = a/2

Therefore, the distance between Cl^– ions = (2 x (a/2)^2)^1/2

0.308 = (2 x (a/2)^2)^1/2

0.094864 = 2 x (a/2)^2

0.047432 = (a/2)^2

0.218 = (a/2)

a = 0.432 nm = 4.32 Å.

Right option is (a) 2700 kg m^-3

The EXPLANATION is: Given,

Atomic mass (M)=27 amu

For FCC structure, Z=4

Avogadro’s NUMBER (N0) = 6.02 X 10^23

Edge length of the Al unit cell (a)= 4.05 x 10^-10m

The density of aluminium (ρ) = (Z x M)/(a^3 X N0)

= (4 x 27)/((4.05 x 10^-10) ^3 x 6.02 x 10^23)

= 2700 kg m^-3.

Right CHOICE is (d) BRITTLE

The explanation: METALS are lustrous, ductile and MALLEABLE. They cannot be brittle. Non-metals tend to be brittle in their solid STATE.

Right OPTION is (c) They are isotropic

Explanation: AMORPHOUS solids are isotropic that is they have identical properties in all DIRECTIONS, whereas crystalline solids are ANISOTROPIC that is they have DIFFERENT properties in different directions.

Right CHOICE is (d) orthorhombic

The BEST explanation: In orthorhombic crystal system, all three AXES are unequal in length and all are perpendicular to one another. It is ALSO called as rhombic crystal system. TOPAZ, barite are some examples of orthorhombic crystals.

The correct answer is (a) dipole-dipole interactions

The best explanation: Molecular SOLIDS are solids that are collections of molecules held together by INTERMOLECULAR forces. In polar molecules such as HCl, So2, ETC., the molecules are held together by dipole-dipole interactions.

Correct choice is (a) SCHOTTKY DEFECT

Easy explanation: A vacancy defect is when an atom, ion or molecule is absent from its position in the lattice. When this OCCURS for ionic SOLIDS, it is called a Schottky defect. Cations and anions are found to be absent in stoichiometric proportion so that the electrical neutrality of the CRYSTAL is maintained.

The correct OPTION is (c) 127.0 PM

The EXPLANATION is: Given,

Interionic radius (r) = 55 pm

Edge length (a) =?

For BCC, r = \(\BIG(\frac{\sqrt{3}}{4}\Big)\) x a

Or a = \(\Big(\frac{4}{\sqrt{3}}\Big)\) x r= 4 x 55/1.732 = 127 pm.

Right CHOICE is (a) 1

Best EXPLANATION: In primitive CUBIC unit cell, atoms are PRESENT only at the corner of the cell. Thus, in actual, only \(\frac{1}{8}\)th of an atom (or ion or MOLECULE) belongs to a particular unit cell. Hence, the total number of atoms in primitive cubic unit cell = 8 × \(\frac{1}{8}\) = 1 atom.

The correct choice is (b) True

To explain: Packing efficiency can never be 100% because in packing calculations all constituent PARTICLES filling up the cubical UNIT CELL are ASSUMED to be spheres.

Right option is (a) 2

To EXPLAIN: In one-dimensional close packing, the constituent particles are assumed to be arranged in a row. Thus, each constituent PARTICLE comes in contact with 2 of its neighbors and thereby giving the COORDINATION number 2.

The correct answer is (c) Sodium

The explanation: Given,

Nearest neighbor distance (d) = 365.9 pm

Density (ρ) = 1.51 g cm^-3

For the BCC structure, nearest neighbor distance (d) is RELATED to the edge length (a) as d=\(\Big(\frac{\sqrt{3}}{2}\Big)\) x a

Or a=\(\Big(\frac{2}{\sqrt{3}}\Big)\) x d = 2/1.732 x 365.9 = 422.5 pm

For BCC structure, Z=2

We know, (ρ) = (Z x M)/(a^3 x N0)

Or M = (ρ x a^3 x N0)/Z

= (1.0016 x 10^6 x (422.5 x 10^-12)^3 x 6.02 x 10^23)/2

= 23 amu

Therefore, the given metal X is Sodium.

The correct OPTION is (a) Conduction band

The BEST explanation: A METALLIC crystal has valence ELECTRONS in the valence band and free moving, delocalized electrons in the conduction band. For a metal, these two bands are very close to each other.

Right choice is (c) 92.59 x 10^23 atoms

The explanation: Given,

DENSITY (ρ) = 8.0 g/cm^3

For FCC structure, Z = 4

Avogadro’s number (N0) = 6.02 x 10^23

Edge length of the UNIT cell (a) = 300 x 10^-10 cm

The density of the element (ρ) = (Z x M)/ (a^3 x N0)

 THEREFORE, the Molar Mass (M) = (ρ x a^3 x N0)/(Z)

= (8.0 x 6.02 x 10^23 x 27.0 x 10^-24) /4

= 32.508 g.

Therefore, 32.508 g of the element CONTAINS 6.02 x 10^23 atoms.

500 g of the element would CONTAIN = (6.02 x 10^23 x 500)/ 32.508 = 92.59 x 10^23 atoms.

Correct answer is (a) Copper

Easy explanation: Copper metal BEARS face-centered unit cells in its crystal STRUCTURE. POTASSIUM and chromium both have body-centered unit cells whereas POLONIUM is the only known metal to bear a simple cubic structure. FCC structure has the highest efficiency.

Right answer is (c) 3.011 X 10^23

For explanation: Atomic mass of Al = 27G/mole (contains 6.022 x 10^23 Al atoms)

Since it exhibits FCC, there are 4 Al atoms/UNIT cell.

If 27g Al contains 6.022 x 10^23 Al atoms then 54G Al contains 1.2044 x 10^24atoms.

Thus, if 1 unit cell contains 4 Al atoms then number of unit cells CONTAINING 1.2044 x 10^24 atoms=(1.2044 x 10^24 x 1)/4 = 3.011× 10^23 unit cells.

Correct answer is (b) Covalent solids

For explanation: Covalent solids consists of a long chain of covalent BONDS between the ADJACENT MOLECULES throughout the crystal. HENCE, they are called giant molecules. They are hard and brittle in NATURE.

The correct OPTION is (c) monoclinic

To elaborate: In monoclinic crystal system, all the THREE AXES are unequal in length and two axes are perpendicular to each other. Gypsum and borax are EXAMPLES of monoclinic crystals.

The correct choice is (d) molecular crystal

For EXPLANATION: Solid CO2 is an example of molecular crystal. These solids have molecules as their CONSTITUENT particles. These solids may be bonded by vander WAALS’ forces or by dipole-dipole attraction or by strong hydrogen bonds. H2, Cl2, I2 are some EXAMPLES of molecular solids.