Chapter 2

Ice crystallizes in hexagonal lattice. At a given temperature, the density of ice is \(0.92 \mathrm{gcm}^{-3}\). The volume of unit cell is \(1.3 \times 10^{-22} \mathrm{~cm}^{3}\). The number of \(\mathrm{H}_{2} \mathrm{O}\) molecules per unit cell is

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 \(\left.6 \times 10^{23}\right)\) is

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

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 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 \(\mathrm{Na}=\) \(23, \mathrm{Cl}=35.5]\) (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 [2005] (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) (a) \(\frac{20}{3} \pi \mathrm{r}^{3}\) (b) \(\frac{24}{3} \pi \mathrm{r}^{3}\) (c) \(\frac{12}{3} \pi \mathrm{r}^{3}\) (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 [2013] (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) \(\mathrm{r}_{\mathrm{Cs}^{+}}+\mathrm{r}_{\mathrm{cl}^{-}}=\sqrt{3} \mathrm{a}\) (c) \(\mathrm{r}_{\mathrm{Cs}^{+}}+\mathrm{r}_{\mathrm{ct}}=3 \mathrm{a}\) (d) \(\mathrm{r}_{\mathrm{Cs}^{+}}+\mathrm{r}_{\mathrm{cl}^{-}}=\frac{3 \mathrm{a}}{2}\)

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 (a) \(1.86 \AA\) (b) \(3.22 \AA\) (c) \(5.72 \AA\) (d) \(0.93 \AA\)

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