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}} $
$ =0.380\text{ }c{{m}^{3}} $
Volume of solid Ar containing
$ 1.65\text{ }g=1\text{ }c{{m}^{3}} $
Empty space $ =1-0.380=0.620 $ % = 62%