Kristen Mcku The Packing of Atoms and Ions in Crystals Note: Please put all the answers in decimal form. Assume the radius of each sphere = 1.00 A. 1. A Study of Metallic Crystals a. Body-Centered Cubic Why is this structure called body-centered cubic? Because the one carbon atom is the center of the cube. What is the coordination number of a sodium atom when packed in a crystal of this type? If this model were extended in all directions, what difference, if any, would there be in the relative position of corner sphere and those in the center? Note: In the calculations below, consider all distances to be measured between the centers of the spheres. From a study of the right triangles involved in a cube, as illustrated below, where (a) is the edge length. (f) is the face diagonal, and (b) is the body diagonal, the following is apparent: a 711 b b² = f² + a² f = a² + a² b² = 3a² In calculating the volumes, not that only one-eighth of each of the corner spheres is inside the cube which has as its corners the centers of the spheres. The volume of a sphere may be calculated from its radius by using the formula: V = 4/3лr³ 1 Kristen Mcku The Packing of Atoms and Ions in Crystals Note: Please put all the answers in decimal form. Assume the radius of each sphere = 1.00 A. 1. A Study of Metallic Crystals a. Body-Centered Cubic Why is this structure called body-centered cubic? Because the one carbon atom is the center of the cube. What is the coordination number of a sodium atom when packed in a crystal of this type? If this model were extended in all directions, what difference, if any, would there be in the relative position of corner sphere and those in the center? Note: In the calculations below, consider all distances to be measured between the centers of the spheres. From a study of the right triangles involved in a cube, as illustrated below, where (a) is the edge length. (f) is the face diagonal, and (b) is the body diagonal, the following is apparent: a 711 b b² = f² + a² f = a² + a² b² = 3a² In calculating the volumes, not that only one-eighth of each of the corner spheres is inside the cube which has as its corners the centers of the spheres. The volume of a sphere may be calculated from its radius by using the formula: V = 4/3лr³ 1