A metal crystallizes into two cubic phases, face-centred cubic (fcc) and body-centred cubic (bcc) whose unit cell lengths are 3.6 and 3.0 Å, respectively. Calculate the ratio of densities of fcc and bcc.

Ans.   fcc unit cell length =3.6 ÅBcc unit cell length  =3.0 ÅDensity in fcc=n1×atomic massV1×Av. no.Density in bcc =n2×atomic massV2×Av. no.DfccDbcc=n1n2×V2V1Now, n1 for fcc = 4; Also, V1=a3=(3.6×10−8)3n2 for bcc = 2; Also,V2=a3=(3.0×10−8)3DfccDbcc=4×(3.0×10−8)32×(3.6×10−8)3=1.16