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The density of solid argon is 1.65g//mL ...

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)`

A

26

B

32

C

68

D

52

Text Solution

Verified by Experts

The correct Answer is:
C
Volume of one atom of `Ar=(4)/(3)pir^(3)`
Also, No. of atom in 1.65kg
`=(1.65)/(40)xx6.023xx10^(25)`
`therefore` Total volume of all atoms of Ar in solid state
`=(4)/(3)pir^(3)xx(1.65)/(40)xx6.023xx10^(23)`
`=(4)/(3)xx(22)/(7)xx(1.54xx10^(-4))^(3)xx(1.65)/(40)xx6.023=0.380cm^(3)`
Volume of solid argon=`1cm^(3)`
`therefore %` empty space `=([1-0.380])/(1)xx100=62%`
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