SCH4U Lee 1.6

The element rhodium (Rh) crystallizes with a Face Centered Cubic unit cell. The metallic radius of a rhodium atom is 134 pm. Use this information to calculate the theoretical density of rhodium atom in g/cm3. 1 pm = 1×10−12 meters.[Note: The theoretical value for the density may be different from the experimentally determined value. Simply Googling the value of density may not yield the correct result]Answer in g/cm3

The element manganese (Mn) crystallizes with a Body Centered Cubic unit cell. The metallic radius of a manganese atom is 137 pm. Use this information to calculate the theoretical density of manganese atom in g/cm³. 1 pm = 1×10-¹2 meters. [Note: The theoretical value for the density may be different from the experimentally determined value. Simply Googling the value of density may not yield the correct result] g/cm³

1. Simple Cubic Unit Cell a. Consider one unit cell and assume the length of the side of the cube is "a". Remember that “a" is the distance between the centers of two adjacent atoms. How long is “a", the edge of a unit cell, in terms of radius, r, of an atom? b. A simple cubic cell has the equivalent of only 1 atom. Recall the volume of sphere with radius, r, is expressed as V = 4/3 r. With this information, find the total volume of all the spheres in this unit cell, expressed in terms of r. To do this, take the total number of atoms and multiply it by the volume of one atom, with radius, r) c. Find the volume of the entire unit cell including the empty space in terms of r. Remember for a cube the volume, V=1 xw xh. You already know the edge length of the side in terms of "r" based in the earlier questions. d. Find the fraction of the total volume of the cube (which is the unit cell's volume) is occupied by the atoms. Express this as percent and write your answer in the summary table.