Question

The density of solid argon is 1.65 g per cc at $-233{}^{\circ }C$ . If the argon atom is assumed to be a sphere of radius $1.54\times {10}^{-8}cm,$ the percentage of empty space in solid argon is

• A. 32%
• B. 54%
• C. 68%
• D. 62%

Answer 1

Answer: (D)

Volume of one atom $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times {(1.54\times {10}^{-8})}^{3}c{m}^3$
$=1.53\times {10}^{-23}c{m}^3$
Volume of all atoms in 1.65 g Ar
$=\frac{165}{40}\times 6.02\times {10}^{23}\times 1.53\times {10}^{-23}c{m}^3$
$=0.380c{m}^3$
Volume of solid Ar containing
$1.65g=1c{m}^3$
Empty space $=1-0.380=0.620$ % = 62%