Chapter 2

What will be the distance between two nearest neighbour in primitive, fcc and bcc unit cell? (a) For bcc, \(\mathrm{d}=1.414 \mathrm{a}\) (b) For bcc, \(\mathrm{d}=1.726 \mathrm{a}\) (c) For primitive, \(\mathrm{d}=\mathrm{a}\) (d) For fcc, \(\mathrm{d}=0.707 \mathrm{a}\)

\(\mathrm{Fe}_{3} \mathrm{O}_{4}\) has spinal structure. Which is not true about this solid? (a) Number of \(\mathrm{O}^{2-}>\mathrm{Fe}^{3+}>\mathrm{Fe}^{2+}\) (b) Coordination number of \(\mathrm{Fe}^{3+}=8\) through out the unit cell. (c) \(\mathrm{Fe}^{3+}\) ions are equally distributed between octahedral and tetrahedral voids. (d) Tetrahedral voids are equally distributed between \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) ions.

Match the following: $$ \begin{array}{ll} \hline \text { Column-I } & \text { Column-II } \\ \text { (Unit cell type) } & \text { (Unit cell shapes) } \\ \hline \text { (a) Simple or Primitive } & \text { (p) Cubic } \\ \text { (b) Body centered } & \text { (q) Orthorhombic } \\ \text { (c) Face centred } & \text { (r) Tetragonal } \\ \text { (d) End centred } & \text { (s) Monoclinic } \\ & \text { (t) Triclinic } \\ \hline \end{array} $$

Match the following: $$ \begin{array}{ll} \hline \text { Column-I (Unit cell) } & \begin{array}{l} \text { Column-II } \\ \text { (Property) } \end{array} \\ \hline \text { (a) Primitive cubic } & \text { (p) Packing fraction }< \\ & 0.74 \\ \text { (b) } \mathrm{FCC} & \text { (q) Octahedral void } \\ \text { (c) } \mathrm{BCC} & \text { (r) Tetrahedral void } \\ \text { (d) Primitive hexagonal } & \text { (s) Cubical void } \\ & \text { (t) Co-ordination } \\ & \text { number }<12 . \\ \hline \end{array} $$

Density of Palladium (At wt. \(=106.4\) ) is \(12.0 \mathrm{~g} / \mathrm{cc}\). The unit cell edge length is \(3.9 \times 10^{-8} \mathrm{~cm}\). The effective number of atoms in the unit cell (Avogadro number is \(6 \times 10^{23}\) ) is

In \(\mathrm{CsCl}\) structure, the number of \(\mathrm{Cs}^{+}\)ions that occupy second nearest neighbor locations of a \(\mathrm{Cs}^{+}\)ion is

133\. The cubic unit cell of aluminium has an edge length of \(400 \mathrm{pm}\). Its density is \(2.8 \mathrm{~g} \mathrm{~cm}^{-3}\). The number of atoms present per unit cell will be \(.\) (atomic mass of \(\mathrm{Al}=27\) )

The \(\mathrm{ZnS}\) structure is cubic. The unit cell may be described as a face centered sulphide ion sub-lattice with zinc ions in the centers of alternating mini cubes made by partitioning the main cube into eight equal parts. The sum of the nearest neighbors around each \(\mathrm{Zn}^{2+}\) and \(\mathrm{S}^{2-}\) ion in the unit cell with be equal to

Number of atoms in the unit cell of \(\mathrm{Na}\) (BCC type crystal) and \(\mathrm{Mg}\) (FCC type crystal) are respectively [2002] (a) 4,4 (b) 4,2 (c) 2,4 (d) 1,1

How many unit cells are present in a cube shaped ideal crystal of \(\mathrm{NaCl}\) of mass \(1.00 \mathrm{~g}\) ? [Atomic mass of \(\mathrm{Na}=\) \(23, \mathrm{Cl}=35.5]\) [2003] (a) \(2.57 \times 10^{21}\) (b) \(6.14 \times 10^{21}\) (c) \(3.28 \times 10^{21}\) (d) \(1.71 \times 10^{21}\)

An ionic compound has a unit cell consisting of A ions at the corners of a cube and \(\mathrm{B}\) ions on the centres of the faces of the cube. The empirical formula for this compound would be \([\mathbf{2 0 0 5}]\) (a) \(\mathrm{AB}\) (b) \(\mathrm{A}_{2} \mathrm{~B}\) (c) \(\mathrm{AB}_{3}\) (d) \(\mathrm{A}_{3} \mathrm{~B}\)

Total volume of atoms present in a face-centred cubic unit cell of a metal is ( \(\mathrm{r}\) is atomic radius) [2006] (a) \(\frac{20}{3} \pi \mathrm{r}^{3}\) (b) \(\frac{24}{3} \pi \mathrm{r}^{3}\) (c) \(\frac{12}{3} \pi r^{3}\) (d) \(\frac{16}{3} \pi \mathrm{r}^{3}\)

In a compound, atoms of element \(\mathrm{Y}\) from ccp lattice and those of element \(\mathrm{X}\) occupy \(2 / 3^{\text {rd }}\) oftetrahedral voids. The formula of the compound will be \([2008]\) (a) \(\mathrm{X}_{4} \mathrm{Y}_{3}\) (b) \(\mathrm{X}_{2} \mathrm{Y}_{3}\) (c) \(\mathrm{X}_{2} \mathrm{Y}\) (d) \(\mathrm{X}_{3} \mathrm{Y}_{4}\)

Copper crystallizes in fcc with a unit cell length of \(361 \mathrm{pm}\). What is the radius of copper atom? [2009] (a) \(127 \mathrm{pm}\) (b) \(157 \mathrm{pm}\) (c) \(181 \mathrm{pm}\) (d) \(108 \mathrm{pm}\)

The edge length of a face centred cubic cell of an ionic substance is \(508 \mathrm{pm}\). If the radius of the cation is 110 \(\mathrm{pm}\), the radius of the anion is (a) \(288 \mathrm{pm}\) (b) \(398 \mathrm{pm}\) (c) \(618 \mathrm{pm}\) (d) \(144 \mathrm{pm}\)

Percentage of free space in cubic close packed structure and in body centered packed structure are respectively \([2010]\) (a) \(30 \%\) and \(26 \%\) (b) \(26 \%\) and \(32 \%\) (c) \(32 \%\) and \(48 \%\) (d) \(48 \%\) and \(26 \%\)

In an face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of \(\mathrm{B}\) is missing from one of the face centred points, the formula of the compound is [2011] (a) \(\mathrm{A}_{2} \mathrm{~B}_{5}\) (b) \(\mathrm{AB}_{2}\) (c) \(\mathrm{A}_{2} \mathrm{~B}\) (d) \(\mathrm{A}_{2} \mathrm{~B}_{3}\)

Lithium forms body centered cubic structure. The length of the side of its unit cell is \(351 \mathrm{pm}\). Atomic radius of the lithium will be (a) \(75 \mathrm{pm}\) (b) \(240 \mathrm{pm}\) (c) \(300 \mathrm{pm}\) (d) \(152 \mathrm{pm}\)

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

Experimentally it was found that a metal oxide has formula \(\mathrm{M}_{0.98} \mathrm{O} .\) Metal \(\mathrm{M}\), is present as \(\mathrm{M}^{2+}\) and \(\mathrm{M}^{3+}\) in its oxide. Fraction of the metal which exists as \(\mathrm{M}^{3+}\) would be (a) \(6.05 \%\) (b) \(5.08 \%\) (c) \(7.01 \%\) (d) \(4.08 \%\)

CsCl crystallizes in body centred cubic lattice. if ' a' is its edge length then which of the following expression is correct: (a) \(\mathrm{r}_{\mathrm{Cs}}+\mathrm{r}_{\mathrm{cT}}=\frac{\sqrt{3}}{2} \mathrm{a}\) (b) \(\mathrm{r}_{\mathrm{Cs}^{*}}+\mathrm{r}_{\mathrm{C}^{-}}=\sqrt{3} \mathrm{a}\) (c) \(\mathrm{r}_{\mathrm{C} s^{+}}+\mathrm{r}_{\mathrm{c}^{-}}=3 \mathrm{a}\) (d) \(\mathrm{r}_{\mathrm{C}^{+}}+\mathrm{r}_{\mathrm{C}]}=\frac{3 \mathrm{a}}{2}\)

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 \([2015]\) (a) \(1.86 \mathrm{~A}\) (b) \(3.22 \AA\) (c) \(5.72 \AA\) (d) \(0.93 \mathrm{~A}\)

Which of the following compounds is metallic and ferromagnetic [2016] (a) \(\mathrm{CrO}_{2}\) (b) \(\mathrm{VO}_{2}\) (c) \(\mathrm{MnO}_{2}\) (d) \(\mathrm{TiO}_{2}\)