The density of solid argon is `1.65g//mL ` at `-233^(@)C` . If the argon atom is assumed to be sphere of radius `1.54xx10^(-8)cm`, what percentage of solid argon is apparentaly empty space ? `(At. Wt. of Ar=40)`

Options

A. 0.54
B. 0.82
C. 0.62
D. 0.48

Answer

C

Explanation

Volume of one atom of Ar `=(4)/(3)pir^(3)`
Also number of atoms in `1.65` g per mL
`=(1.65)/(40)xx6.022xx10^(23)`
`:.` Total volume of all the atoms of Ar in solid state
`=(4)/(3)pir^(3)xx(1.65)/(40)xx6.022xx10^(23)`
`=(4)/(3)xx(22)/(7)xx(1.54xx10^(-8))^(3)xx(1.65)/(40)xx6.022xx10^(23)`
`0.380cm^(3)`
Volume of soild Ar = 1 `cm^(3)`
`:.` % emptyspace `=(1-0.380)/(1)xx100=62%`