A quantitative measure of how efficiently spheres pack into unit cells is called packing efficiency, which is the percentage of the cell space occupied by the spheres. Calculate the packing efficiency of a body-centered cubic cell. Be sure your answer has the correct number of significant digits. The relationship between the edge length (a) and radius (r) of atoms in a body-centered cubic cell is: a= 4r 3 The packing efficiency of a body-centered cubic cell: X S

Sample Exercise 6: Empirical Formula and Density: Ionic Solid The unit cell of a binary compound of copper and oxygen is shown here. Given this image and the ionic radii rcut = 0.74 Å and ro² = 1.26 Å, (a) determine the empirical formula of this compound, (b) determine the coordination numbers of copper and oxygen, (c) estimate the length of the edge of the cubic unit cell, and (d) estimate the density of the compound. Solution (a) To determine the empirical formula we need to determine how many of each type of ion there are per unit cell. O: 8(1/8) + 1 = 2 0²-ions in the unit cell. Cu: 4(1) = 4 Cut ions in the unit cell. Empirical Formula: Cu₂O (b) If we can visually determine the coordination number of one of the ions, we can use Equation 12.1 to determine the coordination number of the other ion. Number of cations per formula unit Number of anions per formula unit anion coordination number cation coordination number Cation coordination number = anion coordination number Copper…

Element Xr (99.88 g/mol) has a BCC unit cell and a density of 16.87 g/cm33.  Based on this information, what is the radius of an atom of Xr in pm?

Metallic uranium crystallizes in a body-centered cubic lattice, with one U atom per lattice point. If the metallic radius of U is 148.5 pm, what is the volume of the unit cell?

Metallic strontium crystallizes in a face-centered cubic lattice, with one Sr atom per lattice point. If the metallic radius of Sr is 215 pm, what is the volume of the unit cell in pm³ and in cm³ ? 3 pmº cm³

In an experiment, you measure the proportion of unit cells that occupied by atoms. For one cell, you measure 52% of the cell i occupied by atoms (with 48% empty space), for another cell, y measure 68% is occupied by atoms (with 32% empty space) ar for a 3rd cell you measure 74% is occupied by atoms and 26% i empty space. Which one of these should be the face-centered cubic arrangement? is ½ of a sphere. There are 6 faces, so this gives a total each 2 edge 52% occupied by atoms 74% occupied by atoms & C. Cell type 68% occupied by atoms none are true Num

) The element Polonium (Po) crystallizes in a simple cubic unit cell. If the radius of the Polonium atom is 135 pm, what is the density of Polonium? (Note: edge length = 2r)

Assume some metal X that has a body- centered cubic lattice with all atoms at lattice points. Its density is 3.11 g/cm3 and its atomic weight is 157.3 amu. From these data, calculate the edge length of a unit cell. Edge length = %3D pm