Question

Niobium has a density of 8.57 g/cm3 and crystallizes with the body-centered cubic unit cell.

Calculate the radius of a niobium atom.

Answer 1

For a body-centered unit cell, you have 2 atoms /cell. Radius can be calculated by the equation:

3d^2 = (4r)^2

We calculate as follows:

V = 1 / (8.57 g/cm^3 ( 1 mol / 92.91 g ) ( 6.022x 10^23 atoms / 1 amol ) ( 1 unit cell / 2 atoms )) = 3.60x10^-23 cm^3
d = 3.30 x 10^-8 cm
r = 1.43x 10^-8 cm