Sodium has a bcc structure with nearest neighbour distance 365.9p…

Question

Sodium has a bcc structure with nearest neighbour distance 365.9pm. Calculate its density (Atomic mass of sodium = 23).

✓

Answer

For the structure, nearest neighbour distance (d) is related to the edge (a) as $\text{d}=\frac{\sqrt{3}}{2}\text{a},$
or, $\text{a}=\frac{2}{\sqrt{3}}\text{d}=\frac{2}{1.732}\times365.9=422.5\text{pm}$
For bcc structure z = 2,
For sodium, M = 23
Density, $\text{d}=\frac{\text{z}\times\text{M}}{\text{a}^3\times\text{N}_{\text{a}}}$
$=\frac{2\times23\text{g/mol}^{-1}}{(422.5\times10^{-10}\text{cm)}^3\times(6.02\times10^{23}\text{mol}^{-1})}=1.013\text{g/cm}^3$

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