The molar gas volume at S.T.P is 22.4 litre and Avogadro's number is `6.023 xx 10^(23)`. Calculate (i) number of gas molecules per unit volume (ii) radius of gas molecule when mean free path is `1.1 xx 10^(-8) m`.

Answer

`2.69 xx 10^(25)m^(-3)`, `4.36 xx 10^(-10)=m`

Explanation

Here , `V = 22.4 litre = 22.4 xx 10^(-3)m^(3)`
`N = 6.023 xx 10^(23)`
`:.n=N/V = (6.023 xx 10^(23))/(22.4 xx 10^(-3)) = 2.69 xx 10^(25)m^(-3)`
Now , `lambda = 1.1 xx 10^(-8) m`
As `lambda = (1)/(sqrt(2)pi d^(2)n)`
`d^(2) = 1/(sqrt(2) pi n lambda)`
`=1/(1.414 xx 3.14xx 2.69 xx 10^(25) xx 1.1 xx 10^(-8))`
`d = 8.72 xx 10^(-10) m`
` r = d/2 = 8.72/2 xx 10^(-10)m = 4.36 xx 10^(-10)=m`