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  4. 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 mathringA respectively. The ratio of densities of lattices fcc to bcc for the metal M is (Nearest integer)

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Q. 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 $2.5 \,\mathring{A}$ respectively. The ratio of densities of lattices fcc to bcc for the metal $M$ is ___ (Nearest integer)

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Solution:

$d =\frac{Z \times M}{N_{ A } a ^3} $
$\frac{ d _{ FCC }}{ d _{ BCC }}=\frac{\frac{4 \times M _{ w }}{ N _{ A } \times(2)^3}}{\frac{2 \times M _{ w }}{ N _{ A } \times(2.5)^3}}=3.90$