Problem 3
How are spheres organized in a body-centred cubic arrangement? How does the body-centred cubic arrangement differ from a simple cubic one?
Problem 4
What is meant by a nearest-neighbour in an assembly of spheres? How many nearest-neighbours does each sphere possess in a (a) cubic close-packed, hexagonal close-packed, (c) simple cubic and body-centred cubic arrangement?
Problem 8
What is meant by solvent of crystallization? The crystallization of \(\mathrm{C}_{60}\) from benzene and diiodomethane yields solvated crystals of formula \(\mathrm{C}_{60} \cdot x \mathrm{C}_{6} \mathrm{H}_{6} \cdot y \mathrm{CH}_{2} \mathrm{I}_{2} .\) If the loss of solvent leads to a \(32.4 \%\) reduction in the molar mass, what is a possible stoichiometry of the solvated compound?
Problem 10
Comment on the relative values of the metallic \((197 \mathrm{pm})\) and ionic radii \((100 \mathrm{pm})\) of calcium.
Problem 11
Account for the following observations: (a) The density of \(\alpha\) -graphite is less than that of diamond. (b) In group \(13,\) the melting point of \beta-rhombohedral B is much higher \((2453 \mathrm{K})\) than that of \(\mathrm{Al}(933 \mathrm{K})\) (c) The group 1 metals tend to exhibit lower values of \(\Delta_{\mathrm{a}} H^{\circ}(298 \mathrm{K})\) than metals in the \(d\) -block.
Problem 12
To what processes do the values of (a) \(\Delta_{\text {fus }} H=0.7 \mathrm{kJ} \mathrm{mol}^{-1},\) (b) \(\Delta_{\text {vap }} H=5.6 \mathrm{kJ} \mathrm{mol}^{-1}\) and \((\mathrm{c}) \Delta_{\mathrm{a}} H^{\circ}=473 \mathrm{kJ} \mathrm{mol}^{-1}\) for nitrogen refer? Discuss the relative magnitudes of the values.
Problem 13
A localized covalent \(\sigma\) -bond is directional, while metallic bonding is non-directional. Discuss the features of covalent and metallic bonding that lead to this difference.
Problem 14
Using simple band theory, describe the differences between electrical conduction in a metal such as lithium and in a semiconductor such as germanium.
Problem 15
(a) What is a band gap? (b) Which of the following would you associate with a metal, a semiconductor and an insulator: (i) a large band \(\operatorname{gap}\) (ii) a very small band gap, (iii) a partially occupied band?
Problem 16
\(\mathrm{ReO}_{3}\) is a structure type. The structure can be described as a simple cubic array of Re atoms with \(\mathrm{O}\) atoms located in the middle of each of the cube edges. Construct a unit cell of \(\mathrm{ReO}_{3}\). What are the coordination numbers of Re and \(\mathrm{O} ?\) Confirm that your unit cell gives the correct stoichiometry for \(\mathrm{ReO}_{3}\).
