Question 12.2.1: Relate edge length and atomic radius for a body-centered cub......
Relate edge length and atomic radius for a body-centered cubic unit cell.
Metallic uranium crystallizes in a BCC lattice, with one U atom per lattice point. How many atoms are there per unit cell? If the edge length of the unit cell is found to be 343 pm, what is the metallic radius of U in pm?
You are asked to determine the number of atoms in a unit cell and the metallic radius of an atom in a unit cell.
You are given the type of unit cell and the edge length of the unit cell.
A BCC lattice has an atom on each corner (each corner shared by eight unit cells) and oneatom completely within the unit cell.
(8 atoms on corner)\frac{1}{8} + 1 atom in center = 2 atoms per unit cell
In this type of lattice the atoms are in contact along the body diagonal.
a = \frac{4\mathcal{r} }{\sqrt{3} }, where r is the metallic radius and α is the edge length of the unit cell
\mathcal{r}=\frac{a \sqrt{3} }{4} =\frac{\left(343\text{ pm}\right)\sqrt{3} }{4} = 149 pm