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  4. Sodium crystallizes in bcc arrangement with the interfacial separation between the atoms at the edge 53 pm. The density of the solid is

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Q. Sodium crystallizes in bcc arrangement with the interfacial separation between the atoms at the edge $53\, pm$. The density of the solid is

AIIMSAIIMS 2009

Solution:

Given, $a-2\, r=53\, pm$
For bcc structure,
$4 r=\sqrt{3} a$
or $ 2 r=\frac{\sqrt{3}}{2} a$
$\Rightarrow a-\frac{\sqrt{3}}{2} a=53$
$\therefore a=395.6 \, pm$
Density $(d)=\frac{Z M}{N_{a} a}$
$d =\frac{2 \times 23}{6.023 \times 10^{23} \times(3.956)^{3} \times 10^{-24}} $
$=1.23 \,g / cc .$