Question

The unit cell for uranium has orthorhombic symmetry, with a, b, and c lattice parameters of 0.286, 0.587, and 0.495 nm, respectively. if its density, atomic weight, and atomic radius are 19.05 g/cm3 , 238.03 g/mol, and 0.1385 nm, respectively, compute the atomic packing factor.

Answer 1

To calculate the atomic packing factor (APF) for uranium in an orthorhombic unit cell, you need to find the volume of the atoms within the unit cell and divide it by the total volume of the unit cell.

Step-by-step explanation:

The atomic packing factor (APF) is a measure of how efficiently atoms are packed within a unit cell of a crystal structure. To calculate the APF, we need to first find the volume of the atoms within the unit cell and then divide it by the total volume of the unit cell. In this case, the atomic packing factor is given by the formula:

APF = (Volume of atoms within the unit cell) / (Total volume of the unit cell)

To calculate the volume of the atoms, we can assume that the uranium atoms are spheres, and we can use the atomic radius to find their volume. The volume of a sphere is given by the formula:

Volume = (4/3) * π * (radius)^3

Since there is only one atom per unit cell in this case, the volume of the atoms within the unit cell is equal to the volume of one uranium atom. We can calculate the atomic packing factor using the given values for the lattice parameters and atomic radius.