Question

Niobium (Nb) has an atomic radius of 0.1430 nm and a density of 8.57 g/cm^3. Determine whether it has an FCC or a BCC crystal structure.

Answer 1

density = 8.57 g/cm3

atomic radius = 0.1430 nm

if Nb is BCC.

4r = sqrt(3)a

a = 4 r /sqrt(3) = 4 x 0.1430 / 1.732

= 0.330 nm

= 0.33 x 10^-7 cm

Atomic mass = 92.906 g/mol

density = Z M / N a^3

            = 2 x 92.906 / 6.023 x 10^23 x (0.33 x 10^-7)^3

            = 8.57 g/cm3

here the density is 8.57 g/cm3

this matches with the given density value. so this is confirmed to be BCC.