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Q.
The cubic unit cell of a metal (molar mass $=63.55 \,\,g \,mol ^{-1}$ ) has an edge length of $362 \,pm$ Its density is $8.92 \,g \,cm ^{-3}$. The type of unit cell is
EAMCETEAMCET 2009
Solution:
Density, $d=\frac{M Z}{N_{0} a^{3}}$
where, $Z=$ number of atoms in unit cell
$ \therefore Z =\frac{d N_{0} a^{3}}{M} $
$=\frac{8.92 \times 6.023 \times 10^{23} \times\left(362 \times 10^{-10}\right)^{3}}{63.55} $
$=4.0 $
Thus, metal has face centred unit cell.