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 Å respectively. Calculate the ratio of the densities of fcc and bcc.

A metal crystallizes into two cubic phases, face- centred cubic (fcc)

1.	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 Å respectively. Calculate the ratio of the densities of fcc and bcc.
Answer» Solution :Denstiy ` (p) = ( Z XX M)/(a^(3) xx N_(0)) ` ForZ = 4,a = 3.5 Å= 3.5 Å= 3.5 ` xx 10^(-8)`cm . ` p_("fcc")= (4xxM) /((3.5 xx 10^(-8))xx N_(0)) ` for bcc, Z =2 , a = 3.0 Å = 3.0 ` xx 10^(-8)`cm `p_("bcc")= ( 2xx M)/((3.0 xx10^(-8))^(3) xx N_(0)) therefore p_("fcc")/p_("bcc") = ( 4XX (3.0 xx 10^(-8))^(3))/(2xx (3.5 xx10^(-8))^(3) ) =1.259`