Problem 38
Define the following terms: crystalline solid, lattice point, unit cell, coordination number, closest packing.
Problem 39
Describe the geometries of the following cubic cells: simple cubic, body- centered cubic, face-centered cubic. Which of these structures would give the highest density for the same type of atoms? Which the lowest?
Problem 40
Classify the solid states in terms of crystal types of the elements in the third period of the periodic table. Predict the trends in their melting points and boiling points.
Problem 41
The melting points of the oxides of the third-period elements are given in parentheses: \(\mathrm{Na}_{2} \mathrm{O}\left(1275^{\circ} \mathrm{C}\right)\) \(\mathrm{MgO}\left(2800^{\circ} \mathrm{C}\right), \mathrm{Al}_{2} \mathrm{O}_{3}\left(2045^{\circ} \mathrm{C}\right), \mathrm{SiO}_{2}\left(1610^{\circ} \mathrm{C}\right), \mathrm{P}_{4} \mathrm{O}_{10}\) \(\left(580^{\circ} \mathrm{C}\right), \mathrm{SO}_{3}\left(16.8^{\circ} \mathrm{C}\right), \mathrm{Cl}_{2} \mathrm{O}_{7}\left(-91.5^{\circ} \mathrm{C}\right) .\) Classify these solids in terms of crystal types.
Problem 43
Write the Bragg equation. Define every term and describe how this equation can be used to measure interatomic distances.
Problem 44
What is the coordination number of each sphere in (a) a simple cubic cell, (b) a body-centered cubic cell, and (c) a face-centered cubic cell? Assume the spheres are all the same.
Problem 45
Calculate the number of spheres that would be found within a simple cubic cell, body-centered cubic cell, and face-centered cubic cell. Assume that the spheres are the same.
Problem 46
Metallic iron crystallizes in a cubic lattice. The unit cell edge length is \(287 \mathrm{pm}\). The density of iron is \(7.87 \mathrm{~g} /\) \(\mathrm{cm}^{3}\). How many iron atoms are within a unit cell?
Problem 47
Barium metal crystallizes in a body-centered cubic lattice (the Ba atoms are at the lattice points only). The unit cell edge length is \(502 \mathrm{pm}\), and the density of the metal is \(3.50 \mathrm{~g} / \mathrm{cm}^{3}\). Using this information, calculate Avogadro's number. [Hint: First calculate the volume (in \(\mathrm{cm}^{3}\) ) occupied by \(1 \mathrm{~mole}\) of \(\mathrm{Ba}\) atoms in the unit cells. Next calculate the volume (in \(\mathrm{cm}^{3}\) ) occupied by one \(\mathrm{Ba}\) atom in the unit cell. Assume that 68 percent of the unit cell is occupied by \(\mathrm{Ba}\) atoms.
Problem 48
Vanadium crystallizes in a body-centered cubic lattice (the \(\mathrm{V}\) atoms occupy only the lattice points). How many \(\mathrm{V}\) atoms are present in a unit cell?
