Answer : The molecular diameter is, [tex]2.179\times 10^{-8}cm[/tex][/tex]
Explanation :
Formula used for mean free path :
[tex]\lambda=\frac{1}{\sqrt{2}\pi d^2(\frac{N}{V})}[/tex]
where,
[tex]\lambda[/tex] = Mean free path = [tex]1.51\times 10^{-5}cm[/tex]
d = diameter of molecule = ?
[tex]\frac{N}{V}[/tex] = number of molecules per unit volume = [tex]3.41\times 10^{19}molecules/cm^3[/tex]
Now put all the given values in this formula, we get:
[tex]1.51\times 10^{-5}cm=\frac{1}{\sqrt{2}\times (3.14) (d)^2\times (3.14\times 10^{19})}[/tex]
[tex]d=2.179\times 10^{-8}cm[/tex][/tex]
Therefore, the molecular diameter is, [tex]2.179\times 10^{-8}cm[/tex][/tex]
