Question

Magnesium (Mg) has an HCP crystal structure, a c/a ratio of 1.624, and a density of 1.74 g/cm^3. Compute the atomic radius for Mg.

Answer 1

Mg hcp c/a = 1.624
hcp is close-packed example ABABAB etc
V = sin(60)*a*a*1.624 a
V = 1.624 *0.866*a^3
V = 1.406*a^3 cm3
Z = 2 (atoms inside unit cell)
Mass inside unit cell is = (2 * 24.303)/(6.022*10^23) = 8.071*10^-23 g
D =M/V
1.74 = 8.071*10^-23/1.406*a^3
a^3 = 8.071*10^-23/1.406*1.74 = 3.299*10^-23
a = 3.207*10-8 = 320.7 pm

hcp unit cell you can see that that the spheres touch each other along
so 2rMg = a where rMg is the radius of a Mg ion and = 160.4 pm