The diameter of an oxygen molecule is 3 `Ã…` The ratio of molecular volume to the actual volume occupied by the oxygen gas at STP is

Options

A. `6xx10^(-28)`
B. `8xx10^(-4)`
C. `4xx10^(-10)`
D. `4xx10^(-4)`

Answer

B

Explanation

`r_0 = 1.5 xx 10^(-10) m` ,
In 22.4 litres i.e. `22.4 xx 10^(-3) m^(-3)`,
There are `N_A = 6.23 xx 10^(23)` molecules
Total volume of oxygen molecules ` = 2 xx 4/3 pi r^3 xx N_A`
Fraction of volume occupied
`= (2 xx 4/3xx pi xx(1.5 xx 10^(-10))^3 xx 6.023 xx 10^23)/((22.4 xx 10^(-3))) = 8xx 10^(-4)`