HON 225 October 13, 2014 Please print Quiz #4: 50 pts 1. (4 pts) Match each type of crystal bonding with the correct definition. a. 4 Covalent 1. Has the weakest bonds between particles b. 2 Metallic 2. All particles in this solid are cations c. 1 Molecular 3. Held together via electrostatic forces d. 3 Ionic 4. Electrons are shared evenly between particles 2. (6 pts) Answer the following true or false questions. Please print clearly. a. F Face-centered cubic structures have the equivalent of five atoms per unit cell. b. T Both hexagonal closest packing and cubic closest packing have coordination numbers of 12. c. F The corner atoms touch one another in the body centered cubic structure. 3. (6 pts) There are several different types of crystal defects. Pick two and provide a description. Sketches might help. Types of defects include: (1) Edge defects: disorder because attraction to surrounding crystal components changes at the edge of a crystal (2) Vibrational defects: bonds lengths change constantly due to vibrations, causing short-lived defects (3) Impurities: air or fluids (small or large) can lodge within a lattice or displace atoms or ions in a normal lattice. E.g. amethyst is purple because of the Fe impurity in quartz. Impurities can result in mis-ordering of atoms or ions within the structure. Impurities can be interstitial or substitutional. (4) Vacancies: missing atoms or ions. Sometimes replaced with electrons. This results from radiation damage: radiation causes ionization of some atoms. If gaseous, the atoms can diffuse from the crystal, leaving the excited state electrons behind. If the energy levelsassociated with these excited electrons are within the visible region of the spectrum, the crystals can be colorful. (5) Dislocation: Particles are out of position, leading the crystal to grow off into a new direction. 4. (3 pts) Rank the three cubic packing structures (simple cubic, body-centered cubic, face-centered cubic) in order of increasing packing efficiency (i.e., in order of decreasing percent empty space). Simple cubic , Body-centered cubic , Face-centered cubic Lowest efficiency (most empty space) Highest efficiency (least empty space) 5. (6 pts) Match the following. There are two numbered answers for each letter a-c. a. 1, 6 face-centered cubic 1. Same as cubic closest packing b. 2, 4 simple cubic 2. Only one element uses this c. 3, 5 body-centered cubic 3. About one third of metals have this 4. Coordination number = 6 5. Coordination number = 8 6. Coordination number = 126. (12 pts) Many alkaline earth metals for crystalline solids using a BCC structure. If an atom has a radius r, answer the following (express numerical answers to the tenths place). b2 = f2 + a2 f2 = a2 + a2 For a sphere, Volume = (4/3)πr3 a. (2 pts) What is the body diagonal length b in terms of atom radius r? 4r b. (2 pts) What is the edge length of the unit cell, a, in terms of r? 4r / √3 = 2.3r c. (2 pts) What is the total volume of the unit cell, in terms of r? (4r / √3)3 = 12.3r3 d. (2 pts) How many atom volumes are contained within in a BCC unit cell? 2 e. (2 pts) What is the occupied volume of the unit cell in terms of r? 2 x (4/3) x π x r 3 = 8.4 r 3 f. (2 pts) Calculate the percent empty space in this unit cell. 100% – [8.4 r3 / 12.3 r3 x 100%] = 31.7% aaabf7. (13 pts) Solid argon (Ar) forms a SC structure, with a unit cell edge length of 1.94 x 10–8 cm and atomic radius 9.7 x 10–9 cm. Answer the following questions about the crystal structure, using actual values and giving appropriate units. Limit your responses to no more than two significant figures [Volume of a sphere = (4/3)πr3]. a. (2 pts) Total volume of one unit cell (show calculation) 7.3 x 10–24 cm3 Volume = (1.94 x 10–8 cm)3 = 7.3 x 10–24 cm3 b. (1 pts) Number of atoms per unit cell 1 c. (3 pts) Occupied volume of unit cell (show calculation) 3.8 x 10–24 cm3 (i.e., total volume of atoms in unit cell) Volume = 1 x (4/3)π(9.7 x 10–9 cm)3 = 3.8 x 10–24 cm3 d. (2 pts) Empty volume of unit cell (show calculation) 3.5 x 10–24 cm3 (7.3 x 10–24 cm3) – (3.8 x 10–24 cm3) = 3.5 x 10–24 cm3 e. (2 pts) Percent empty space (show calculation) 48% (3.5 x 10–24 cm3) / (7.3 x 10–24 cm3) x 100% = 47.6% f. (3 pts) The mass of a single Ar atom is 6.6 x 10–23 g. What is the density of solid Ar? (show calculation) Density = mass / volume = (6.6 x 10–23 g) / (7.3 x 10–24 cm3) 9.0 g/cm3 = 9.0