Rhodium crystallizes in a face-centered cubic unit cell. The radius of a rhodium atom is 135 pm. Determine the density of rhodium in g/cm3

Density of unit cell ( rhodium) = 12.279 g/cm³

Explanation:

Given that:

The radius (r) of a rhodium atom = 135 pm

The atomic mass of rhodium = 102.90 amu

For a face-centered cubic unit cell,

where;

a = edge length.

Making "a" the subject of the formula:

a = 381.8 pm

to cm, we get:

a = 381.8 × 10⁻¹⁰ cm

However, recall that:

where;

mass of unit cell = mass of atom × numbers of atoms per unit cell

Also;

Recall also that number of atoms in a unit cell for a  face-centered cubic = 4

So;

mass of unit cell = 6.83380375 × 10⁻²² g

Density of unit cell ( rhodium) = 12.279 g/cm³