# PRACTICE PROBLEMS

## Crystal Structure

1. How many atoms are considered to be present in a simple cubic unit cell?
 a) 1 b) 2 c) 4 d) 9 e) 14
2. How many atoms are considered to be present in a body-centered cubic unit cell?
 a) 1 b) 2 c) 4 d) 9 e) 14
3. How many atoms are considered to be present in a face-centered cubic unit cell?
 a) 1 b) 2 c) 4 d) 9 e) 14
4. Iron metal (Fe) has a body-centered cubic crystal structure with an edge length of 2.866 A. From the edge length, the atomic weight of iron and Avogadro's number (which is the number of items in a mole) it is possible to calculate the density of iron. What is the density of iron?
 a) 3.939 g/cm3 b) 7.879 g/cm3 c) 15.76 g/cm3 d) 25.19 g/cm3 e) 31.85 g/cm3
5. Nickel (Ni) has a face-centered cubic unit cell. The density of nickel is 8.91 g/cm3. From this and the mass of a nickel atom (which can be calculated from the atomic weight and Avogadro's number) it is possible to calculate the edge length of a nickel unit cell. Which of the following is the correct edge length of the nickel unit cell?
 a) 1.175 A b) 2.150 A c) 3.524 A d) 4.515 A e) 5.221 A
6. Tungsten (W) crystalizes in one of the cubic lattice structures -- that is, it is either simple cubic, body-centered cubic, or face-centered cubic. Using the atomic weight of tungsten, Avogadro's number, the fact that the edge length of the tungsten unit cell is 3.165 A, and the fact that the density of tungsten is 19.26 g/cm3, decide which of the 3 possible cubic lattices tungsten has.
 a) simple cubic b) body-centered cubic c) face-centered cubic
7. There is a certain element that has a density of 22.42 g/cm3 and a face-centered cubic lattice with an edge length of 3. 839 A. Which element is it? Hint: Calculate the mass of an atom of this element. Then you can multiply the mass per atom by Avogadro's number to get the atomic weight and look in the periodic table to see which element has this atomic weight. The element is:
 a) lead b) copper c) gold d) chromium e) iridium