Question

Calcium crystallizes in a cubic unit cell with density $3.2$ g/cc. Edge-length of the unit cell is $437$ pm. The nearest neighbour distance (in pm) is :

• A. $154.5$
• B. $309$
• C. $218.5$
• D. $260$

Answer 1

The correct option is B $309$

$d=\frac{zM}{N_A\times V}$
$3.2=\frac{z\times 40}{6.023\times {10}^{23}\times (437\times {10}^{-10}{)}^3}$
$z=\frac{3.2\times 6.023\times 83.4\times {10}^6\times {10}^{-7}}{40}$
$z=4$
$⟹$ Calcium crystallizes in FCC.
$a=2\sqrt{2}r$
$⟹2r=309$ pm