A metal M crystallizes into two lattices :- face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of 2 . 0 and 2 . 5 A ° respectively. The ratio of densities of lattices fcc to bec for the metal M is _______(Nearest integer)

Question

A metal M crystallizes into two lattices :- face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of 2 . 0 and 2 . 5 A ° respectively. The ratio of densities of lattices fcc to bec for the metal M is _______(Nearest integer),

MARKS App · Accepted Answer

The density of the crystal lattice can be calculated as follows, d = Z × M N A a 3 Z = effective number of atoms in unit cell(For BCC=2 and FCC=4) M = Molar mass N A =Avogadro's number a = Edge length d FCC d BCC = 4 × M w N A × ( 2 ) 3 2 × M w N A × ( 2 . 5 ) 3 = 3 . 90

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