Question

CHIM 2045-Other Toolbox #3: Student Name: Solids- Cubic Unit Cell Type Problems Sect. Date: the three tvpes of cubic unit cells, giving in addition for each case: a. The net number of atoms contained within a unit cell: b. The total number of different atoms that contribute to the volume of this type of unit cell 6 Cubic Type: Net # Atom/Unit Cell # of Diff. Atorns/Unit Cell U.C.L Packing EfficiencyPacking Efficiency Cubic Type: Net #Atom/Unit Cell-A-_ # of Diff. Atoms/Unit Cell_ Cubic TypeL Net #Atom/Unit Cell # of Diff. Atoms/Unit Cell U.C.L. 0 Packing Efficiency The most stable solid form of phosphorus arranges itself in a simple cubic type unit cell crystalline lattice. If all the P atoms, each of radius 1.100 x 103 cm are assumed to b 2. e rigid spheres in contact with each other, what is the density of the nonmetal phosphorus (g/cm? (atoms on the corners touch) 3. In metallic silver, slver atoms (Ag) are packed in a face-centered cubic arrangement. If a unit eell's edge length is 4.078 x 108 cm, calculate the density of metallic silver (g/em3). (atoms on a face diagonal touch) 4. Sodium (Na) metal atoms crystallize in a body-centered cubic arrangement. If the sodium's unit cell length (em) is 4,24 x 103 cm, what is metallic sodium's density (g/em3)? (atoms on the front to back diagonal of the cube touch)

Answer 1

Simple cubic cell Net atom = 8 times 1/8 = 1 diffAtom/unit cell = 8 U. C . L = 2R Packing efficiency = 52% Body centered cell Net atom = 1 + 8 times 1/8 = 2 Diff Atom/unit cell = 8 U. C. L = 4/squareroot 3 R Packing efficiency = 68% face centered cell Net atom = 6 times 1/2 + 8 times 1/8 = 4 Diff Atom/unit cell = 12 U. C. L = squareroot 8 R packing efficiency = 74 % (2) Radius = 1.100 times 10^-8 cm a = 2r Atomic weight of phosphorus = 30.9737 g/mol for S. C. C the volume is = (2R)^3 density = nA/V_c Na = (1 atom/unit cell)(30.9737 g/mol)/(2 times 1100 times 10^-8 cm/unit cell)^3 (6.02 times 10^23 atom/mol) = 30.9737 g/6.410096 = 4.832 g/cm^3 (3) radius = 4.078 times 10^-8 cm implies a = squareroot 8 Atomic weight of silver = 107.9 g/mol for F.C.C volume is