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# At room temperature ,sodium crystallises in a body-centred cubic lattice with $a=4.24A^{\large\circ}$.The theoretical density of sodium (At.wt of Na=23) is ?

$\begin{array}{1 1}1.002gcm^{-3}\\2.002gcm^{-3}\\3.002gcm^{-3}\\4.002gcm^{-3}\end{array}$

A body-centred cubic unit cell contains 8 atoms at the 8 corners and one in the center.
$\therefore$ Total number of atoms per unit cell =$8+\large\frac{1}{8}$$+1=2$
Density =$\large\frac{n\times at.wt}{av.no.\times a^3}$
$\Rightarrow \large\frac{2\times 23}{6.023\times 106{23}\times (4.24 \times 10^{-8})^3}$
$\Rightarrow 1.002gcm^{-3}$