Chapter 15

\(\mathrm{X}\) ' melts at low temperature and is a bad conductor of electricity in both liquid and solid state. \(X\) is: (a) Zinc sulphide (b) Mercury (c) Silicon carbide (d) Carbon tetrachloride

A crystal is made up of metal ions ' \(\mathrm{M}_{1}^{\prime}\) and ' \(\mathrm{M}_{2}{\underline{\phantom{xx}}}^{\prime}\) and oxide ions. Oxide ions. form a ccp lattice structure. The cation ' \(\mathrm{M}_{1}\) ' occpies \(50 \%\) of octahedral voids and the cation ' \(\mathrm{M}_{2}\) ' occupies \(12.5 \%\) of tetrahedral voids of oxide lattice. The oxidation numbers of ' \(\mathrm{M}_{1}\) ' and ' \(\mathrm{M}_{2}\) ' are, otivel (a) \(+2,+4\) (b) \(+1,+3\) (c) \(+3,+1\) (d) \(+4,+2\)

A diatomic molecule \(X_{2}\) has a body-centred cubic \((b c c)\) structure with a cell edge of \(300 \mathrm{pm}\). The density of the molecule is \(6.17 \mathrm{~g} \mathrm{~cm}^{-3}\). The number of molecules present in \(200 \mathrm{~g}\) of \(\mathrm{X}_{2}\) is : (Avogadroconstant \(\left.\left(\mathrm{N}_{\mathrm{A}}\right)=6 \times 10^{23} \mathrm{~mol}^{-1}\right)\) (a) \(40 \mathrm{~N}_{\mathrm{A}}\) (b) \(8 \mathrm{~N}_{\mathrm{A}}\) (c) \(4 \mathrm{~N}_{\mathrm{A}}\) (d) \(2 \mathrm{~N}_{\mathrm{A}}\)

Which primitive unit cell has unequal edge lengths (a \(\square \mathrm{b} \square \mathrm{c})\) and all axial angles different from \(90^{\circ}\) ? (a) Triclinic (b) Hexagonal (c) Monoclinic (d) Tetragonal

An element crystallises in a face-centred cubic \((f c)\) unit cell with cell edge \(a\). The distance between the centres of two nearest octahedral voids in the crystal lattice is : (a) \(\frac{a}{\sqrt{2}}\) (b) \(a\) (c) \(\sqrt{2} a\) (d) \(\frac{a}{2}\)

All of the following share the same crystal structure except. (a) \(\mathrm{RbCl}\) (b) \(\mathrm{NaCl}\) (c) \(\mathrm{CsCl}\) (d) \(\mathrm{LiCl}\)

Which of the following compounds is likely to show both Frenkel and Schottky defects in its crystalline form? (a) \(\mathrm{AgBr}\) (b) \(\mathrm{CsCl}\) (c) \(\mathrm{KBr}\) (d) \(\mathrm{ZnS}\)

In a monoclinic unit cell, the relation of sides and angles are respectively: (a) \(\mathrm{a}=\mathrm{b} \neq \mathrm{c}\) and \(\alpha=\beta=\gamma=90^{\circ}\) (b) \(a \neq b \neq c\) and \(\alpha=\beta=\gamma=90^{\circ}\) (c) \(\mathrm{a} \neq \mathrm{b} \neq \mathrm{c}\) and \(\beta=\gamma=90^{\circ} \neq \alpha\) (d) \(\mathrm{a} \neq \mathrm{b} \neq \mathrm{c}\) and \(\alpha \neq \beta \neq \gamma \neq 90^{\circ}\)

Which of the following exists as covalent crystals in the solid state? (a) Iodine (b) Silicon (c) Sulphur (d) Phosphorus

A compound of formula \(\mathrm{A}_{2} \mathrm{~B}_{3}\) has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms: (a) hcp lattice \(-\mathrm{A}, \frac{2}{3}\) Tetrahedral voids \(-\mathrm{B}\) (b) hcp lattice \(-\mathrm{A}, \frac{1}{3}\) Tetrahedral voids \(-\mathrm{B}\) (c) hcp lattice \(-\mathrm{B}, \frac{2}{3}\) Tetrahedral voids \(-\mathrm{A}\) (d) hcp lattice \(-\mathrm{B}, \frac{1}{3}\) Tetrahedral voids \(-\mathrm{A}\)

Copper crystallises in fcc with a unit length of \(361 \mathrm{pm}\). What is the radius of copper atom? (a) \(157 \mathrm{pm}\) (b) \(128 \mathrm{pm}\) (c) \(108 \mathrm{pm}\) (d) \(181 \mathrm{pm}\)

7\. At \(100^{\circ} \mathrm{C}\), copper (Cu) has FCC unit cell structure with cell edge length of \(x \AA\). What is the approximate density of \(\mathrm{Cu}\) (in \(\left.\mathrm{g} \mathrm{cm}^{-3}\right)\) at this temperature? \(\begin{aligned}&\text { [Atomic Mass of } \mathrm{Cu}=63.55 \mathrm{u}] & \text }\end{aligned}\) (a) \(\frac{205}{x^{3}}\) (b) \(\frac{105}{x^{3}}\) (c) \(\frac{211}{x^{3}}\) (d) \(\frac{422}{x^{3}}\)

In which of the following crystals alternate tetrahedral voids are occupied? (a) \(\mathrm{NaCl}\) (b) \(\mathrm{ZnS}\) (c) \(\mathrm{CaF}_{2}\) (d) \(\mathrm{Na}_{2} \mathrm{O}\)

Which type of 'defect' has the presence of cations in the interstitial sites? (a) Schottky defect (b) Vacancy defect (c) Frenkel defect (d) Metal deficiency defect

An element with molar mass \(2.7 \times 10^{-2} \mathrm{~kg} \mathrm{~mol}^{-1}\) forms a cubic unit cell with edge length \(405 \mathrm{pm}\). If its density is \(2.7 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}\), the radius of the element is approximately \(\times 10^{-12} \mathrm{~m}\) (to the nearest integer).

Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS. Column I Column II (A) Simple cubic and (p) have these parameters, face-centered cubic \(\quad a=b=c\) and \(\alpha=\beta=\gamma\) parameters (B) cubic and (q) are two crystal systems rhombohedral (C) cubic and tetragonal (r) have only two crystallographic angles of \(90^{\circ}\) (D) hexagonal and (s) belong to same crystal monoclinic \(\quad\) system

A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is 'a', the closest approach between two atoms in metallic crystal will be: (a) \(2 a\) (b) \(2 \sqrt{2} a\) (c) \(\sqrt{2} a\) (d) \(\frac{a}{\sqrt{2}}\)

Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of \(4.29 \AA\). The radius of sodium atom is approximately (a) \(5.72 \AA\) (b) \(0.93 \AA\) (c) \(1.86 \AA\) (d) \(3.22 \AA\)

The correct statement for the molecule, \(\mathrm{CsI}_{3}\) is (a) It is a covalent molecule. (b) It contains \(\mathrm{Cs}^{+}\)and \(\mathrm{I}_{3}\) ions. (c) It contains \(\mathrm{Cs}^{3+}\) and \(\mathrm{I}^{-}\)ions. (d) It contains \(\mathrm{Cs}^{+}, \mathrm{I}^{-}\)and lattice \(\mathrm{I}_{2}\) molecule.

The appearance of colour in solid alkali meta halides is generally due to: (a) Schottky defect (b) Frenkel defect (c) Interstitial position (d) F-centres

In a face centered cubic lattice atoms A are at the corner points and atoms \(\mathrm{B}\) at the face centered points. If atom \(\mathrm{B}\) is missing from one of the face centered points, the formula of the ionic compound is: (a) \(\mathrm{AB}_{2}\) (b) \(\mathrm{A}_{5} \mathrm{~B}_{2}\) (c) \(\mathrm{A}_{2} \mathrm{~B}_{3}\) (d) \(\mathrm{A}_{2} \mathrm{~B}_{5}\)

Which one of the following statements about packing in solids is incorrect? (a) Coordination number in \(b c c\) mode of packing is 8 . (b) Coordination number in hcp mode of packing is \(12 .\) (c) Void space in \(h c p\) mode of packing is \(32 \%\). (d) Void space is \(c c D\) mode of packing is \(26 \%\)

In a face centred cubic lattice, atoms of A form the corner points and atoms of \(\mathrm{B}\) form the face centred points. If two atoms of \(\mathrm{A}\) are missing from the corner points, the formula of the ionic compound is (a) \(\mathrm{AB}_{3}\) (b) \(\mathrm{AB}_{4}\) (c) \(\mathrm{A}_{2} \mathrm{~B}_{5}\) (d) \(\mathrm{AB}_{2}\)

A substance \(A_{x} B_{y}\) crystallizes in a face centred cubic (FCC) lattice in which atoms 'A' occupy each corner of the cube and atoms 'B' occupy the centres of each face of the cube. Identify the correct composition of the substance \(A_{x} B_{y}\) (a) \(A B_{3}\) (b) \(A_{4} B_{3}\) (c) \(A_{3} B\) (d) Compostion cannot be specified

In a solid ' \(A B\) ' having the \(\mathrm{NaCl}\) structure, ' \(A\) ' atoms occupy the corners of the cubic unit cell. If all the face-centered atoms along one of the axes are removed, then the resultant stoichiometry of the solid is (a) \(A B_{2}\) (b) \(A_{2} B\) (c) \(A_{4} B_{3}\) (d) \(A_{3} B_{4}\)

The coordination number of a metal crystallizing in a hexagonal close-packed structure is (a) 12 (b) 4 (c) 8 (d) 6

CsBr has bcc structure with edge length \(4.3\). The shortest inter ionic distance between \(\mathrm{Cs}^{+}\)and \(\mathrm{Br}^{-}\)is (a) \(3.72\) (b) \(1.86\) (c) \(7.44\) (d) \(4.3\)

Consider an ionic solid \(M X\) with \(\mathrm{NaCl}\) structure. Construct a new structure \((Z)\) whose unit cell is constructed from the unit cell of \(M X\) following the sequential instructions given below. Neglect the charge balance. (i) Remove all the anions \((X)\) except the central one (ii) Replace all the face centered cations ( \(M\) ) by anions \((X)\) (iii) Remove all the corner cations \((M)\) (iv) Replace the central anion \((X)\) with cation \((M)\) The value of \(\left(\frac{\text { number of anions }}{\text { number of cations }}\right)\) in \(Z\) is __ .

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of \(400 \mathrm{pm}\). If the density of the substance in the crystal is \(8 \mathrm{~g} \mathrm{~cm}^{-3}\), then the number of atoms present in \(256 \mathrm{~g}\) of the crystal is \(N \times 10^{24}\). The value of \(N\) is ____ .

The number of hexagonal faces that are present in a truncated octahedron is ___ .

A metal crystallises into two cubic phases, face centered cubic (FCC) and body centred cubic (BCC), whose unit cell lengths are \(3.5\) and \(3.0\) \(\AA\), respectively. Calculate the ratio of densities of \(\mathrm{FCC}\) and \(\mathrm{BCC}\).

Chromium metal crystallizes with a body centred cubic lattice. The length of the unit cell edge is found to be \(287 \mathrm{pm} .\) Calculate the atomic radius. What would be the density of chromium in \(\mathrm{g} / \mathrm{cm}^{3}\) ?

Sodium metal crystallizes in body centred cubic lattice with the cell edge, \(a=4.29 \AA\). What is the radius of sodium atom?

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are) (a) The number of the nearest neighbours of an atom present in the topmost layer is 12 (b) The efficiency of atom packing is \(74 \%\) (c) The number of octahedral and tetrahedral voids per atom are 1 and 2 , respectively (d) The unit cell edge length is \(2 \sqrt{2}\) times the radius of the atom

The correct statement(s) regarding defects in solids is (are) (a) Frenkel defect is usually favoured by a very small difference in the sizes of cation and anion (b) Frenkel defect is a dislocation defect (c) Trapping of an electron in the lattice leads to the formation of F-centre (d) Schottky defects have no effect on the physical properties of solids

Which of the following statement(s) is (are) correct? (a) The coordination number of each type of ion in \(\mathrm{CsCl}\) crystal is 8 . (b) A metal that crystallizes in \(b c c\) structure has a coordination number of \(12 .\) (c) A unit cell of an ionic crystal shares some of its ions with other unit cells. (d) The length of the unit cell in \(\mathrm{NaCl}\) is \(552 \mathrm{pm} .\left(\mathrm{r}_{\mathrm{Na+}}=95 \mathrm{pm} ; \mathrm{r}_{\mathrm{Cl}}=181\right.\) \(\mathrm{pm}\) ).

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space- filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be 'r'. The number of atoms in the HCP unit cell is (a) 4 (b) 6 (c) 12 (d) 17

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space- filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be 'r'. The volume of this \(h c p\) unit cell is - (a) \(24 \sqrt{2} r^{3}\) (b) \(16 \sqrt{2} r^{3}\) (c) \(12 \sqrt{2} r^{3}\) (d) \(\frac{64}{3 \sqrt{3}} r^{3}\)

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space- filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be 'r'. The empty space in this \(h c p\) unit cell is (a) \(74 \%\) (b) \(47.6 \%\) (c) \(32 \%\) (d) \(26 \%\)

Read the following statement (Assertion) and explanation (Reason) and answer each question as per the options given below : (a) If both assertion and reason are correct, and reason is the correct explanation of the assertion. (b) If both assertion and reason are correct, but reason is not the correct explanation of the assertion. (c) If assertion is correct but reason is incorrect. (d) If assertion is incorrect but reason is correct. Assertion : In any ionic solid \([M X]\) with Schottky defects, the number of positive and negative ions are same. Reason : Equal number of cation and anion vacancies are present.

The edge length of unit cell of a metal having molecular weight 75 \(\mathrm{g} / \mathrm{mol}\) is \(5 \AA\) which crystallizes in cubic lattice. If the density is \(2 \mathrm{~g} / \mathrm{cc}\) then find the radius of metal \(\operatorname{atom}\left(N_{A}=6 \times 10^{23}\right)\). Give the answer in \(\mathrm{pm}\)

In face centred cubic \((f c)\) crystal lattice, edge length is \(400 \mathrm{pm}\). Find the diameter of greatest sphere which can be fit into the interstitial void without distortion of lattice.

A compound \(A B\) has rock salt type structure. The formula weight of \(A B\) is \(6.023 Y\) amu, and the closest \(A-B\) distance is \(Y^{1 / 3} \mathrm{~nm}\), where \(Y\) is an arbitrary number. (a) Find the density of lattice (b) If the density of lattice is found to be \(20 \mathrm{~kg} \mathrm{~m}^{-3}\), then predict the type of defect.

The density of mercury is \(13.6 \mathrm{~g} / \mathrm{mL}\). Calculate approximately the diameter of an atom of mercury assuming that each atom is occupying a cube of edge length equal to the diameter of the mercury atom.