Please show step-by-step solution. 2) For a face-centered cube, show the calculation to determine the number of atoms per celland the total number of atoms in 6 unit cells. Page 541 12.3 Unit Cells and Basic Structures541RELATIONSHIPS USED:V = 1³ (Volume of a cube)4r(Edge length of body-centered cubic unit cell)V31 =%3DSOLVESOLUTIONSolve the equation for the volume of a cube for I andsubstitute in the given value for V to find I.V = 131 = Vv = V4.32 × 10-23 cm3.5088 x 10-8 cm%3DSolve the equation for the edge length of a body-centeredcubic unit cell for r and substitute in the value of 1 (from the4r1 =V3previous step) to find r.V31V3 (3.5088 × 10 8 cm)= 1.5193 x 10-8 cm44Convert r from cm to m and then to pm.0.01 m1 pm1.5193 X 10-8 cm x152 pm%3D1 cmW Z1-0CHECK The units of the answer (pm) are correct. The magnitude is reasonable because atomic radii range roughly from 50to 200 pm.FOR PRACTICE 12.3 An atom has radius of 138 pm and crystallizes in the body-centered cubic unit cell. What is thevolume of the unit cell in cm³?The face-centered cubic unit cell (Figure 12.7▼) is a cubeFace-centered cubicwith one atom at each corner and one atom (of the same kind)in the center of each cube face. Note that in the face-centeredunit cell (like the body-centered unit cell), the atoms do nottouch along each edge of the cube. Instead, the atoms touchalong the face diagonal. The edge length in terms of the atomicradius is therefore I = 2V2r, as shown here.62 = 12 + 1? = 21²b = 4r(4r)2 = 212(4r)2%3D%3D124r%3DV2In the face-centered cubic lattice, the atoms touchalong a face diagonal. The edge length is 2V2r.= 2V2rFace-Centered Cubic Unit CellCoordination number = 12Atoms/unit = x 8) + (G x 6) = 4atomatomat 8 cornerSat 6 facesA FIGURE 12.7 Face-Centered Cubic Crystal StructureThe different colors used on the atoms in this figure are forclarity only. All atoms within the structure are identical.

Consider, a single unit cell for face centred cube. In face-centred cubic system, there are two types of atoms: 1) Corner atoms: There are 8 corner atoms and each atom contributes only 1/8th per unit cell. 2) Face centred atoms: There are 6 face centred atoms and each atom contributes 1/2 per unit cell. So, total atoms per unit cell = (1/8) x (Number of corner atoms) + (1/2) x (Number of face atoms) = (1/8) x 8 + (1/2) x 6 = 1 + 3 = 4 Hence, total number of atoms per unit cell = 4 Therefore, Total number of atoms in 6 unit cell = 6 x 4 = 24 atoms