Niobium has an atomic radius of 0143nm and a density of 857

Niobium has an atomic radius of 0.143nm and a density of 8.57 g/cm^3. Determine whether it has FCC or BCC crystal structure.

Solution

Density(d)= Z*M / a³N_A gms/cm³

Here Molecular weight of the Niobium (M)= 93gms/mole, radius (r)=0.143nm =0.143*10^7cm     =1.43*10^-8cm

Let us considor Nb has BCC crystal structure , then edge length(a)=( 4r/?3)= (4*1.43*10^-8)/ 1.732

a = 3.303*10^-8 cm, and Z =2 for BCC

Therefore density (d)= (2*93)/ (3.303*10^-8)³*( 6.023*10^23)

                                     = 186/ 21.704

                                      =8.5698 = 8.57 gms/ cm³

which is exactly matched with the given density of the crystal,hence Niobium is has an BCC crystal structure.