A metal crystallizes into two cubic phases, face centred cubic (fcc) and body centred cubic (bcc), w

Question

A metal crystallizes into two cubic phases, face centred cubic (fcc) and body centred cubic (bcc), whose unit cell lengths are 3.5 and 3.0 $\AA$ respectively. Calculate the ratio of densities of fcc and bcc. (Format: Output the value accurate to two decimal places)

Professor PC Thomas Classes · Answer

Ratio $d_{fcc}/d_{bcc} = (Z_{fcc}/a_{fcc}^3) / (Z_{bcc}/a_{bcc}^3) = (4 / 3.5^3) / (2 / 3.0^3) = (4/42.875) / (2/27) = 0.0933 / 0.0741 = 1.259 \approx 1.26$.