Strontium has density of 2.64 g/cm3 and crystallizes with the face-centered cubic unit cell. part a calculate the radius of a strontium atom.

You are given the density of a strontium atom at 2.64 g/cm3 and crystallizes with the face-centered cubic unit cell. You are asked to find the radius of a strontium atom. Use the density equation where D = M/V. Of course, the M part, because it is focused on the atom part, is equivalent to ZM/A where Z is the number of atoms in a unit cell, M is the molecular weight of the atom and A is the Avogadro's constant. Because it is a face centered cubic cell, the volume would be a³.

In a face center cubic cell, there are 4 atoms. There are eight 1/8 at the corners and six 1/2 on the faces making it 4 atoms. Plugging in all the values to get the side of the cubic cell,

D = [ZM/A]/a³
2.64 grams /cm³ = [(4 atoms)(87.62 grams/mol) / (6.023 x 10²³ atoms/mole)] / a³
a³ = 2.205 x 10⁻²²
a = 6.041 x 10⁻⁸ cm

The relationship between the side of the cube and the radius of the cell is a/r = 2√2 where a is the side of the cube and r is the radius of the atom.

a/r = 2√2
6.041 x 10⁻⁸ cm/r = 2√2
r = 2.136 x 10⁻⁸ cm