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# Vanadium crystallises with a body centered cubic structure with a unit cell of side length $3.011A^{\large\circ}$. Calculate the atomic radius and density (V = 50.94)

$\begin {array}{1,1}(a)\;2.609A^{\large\circ},16.199g/cm^3\\(b)\;1.303A^{\large\circ},16.99g/cm^3\\(c)\;2.609A^{\large\circ},7.200g/cm^3\\(d)\;1.303A^{\large\circ},6.198g/cm^3\end {array}$

Radius to atom in b.c.c = $\large\frac{\sqrt3}{4}\times a$
$=\large\frac{\sqrt3}{4}\times 3.011$
$=1.303A^{\large\circ}$
Density $\rho = \large\frac{n\times at.wt}{Av.no \times a^3}$
$=\large\frac{2\times50.95}{6.023\times10^{23}\times(3.011\times10^{-8})^3}$
$=6.198 g/cm^3$