Question

Sodium (atomic mass $=23$ amu) crystallizes in a bcc arrangement with the interfacial separation between the atoms at the edge $53.6$ pm. The density (in g cm${}^{-3}$) of sodium crystal is:

• A. $2.07$
• B. $2.46$
• C. $1.19$
• D. none of the above

Answer 1

The correct option is C $1.19$

According to given condition,
$a-2R=53.6$ pm
$a(1-\frac{2\left(\sqrt{3}\right)}{4})=53.6$ pm

$⟹a=400$ pm

So, density $=\frac{nM}{V{N}_A}$$=\frac{2\times 23}{(400{)}^3\times 6.023\times {10}^{23}\times {10}^{-24}}=1.19$ g/cc