Answer:
The mean free path is [tex]0.0000373631 m[/tex]
Explanation:
The formula for mean free path is :
λ = [tex]\frac{V}{\sqrt{2}\pi d^{2}N }[/tex]
where,
λ - is the mean free path distance
V - volume of the gas
d - the diameter of the molecule
N - number of molecules.
now ,
density [tex]D[/tex] = [tex]\frac{mass}{volume}[/tex] = [tex]\frac{M}{V}[/tex] ;
mass of the gas = (number of molecules)[tex]*[/tex](mass of one molecule) ;
as it's atomic hydrogen
[tex]M = N*m \\m=1.66*10^{-24}\\M=N*1.66*10^{-24}[/tex]
∴
[tex]D[/tex] = [tex]\frac{N*1.66*10^{-24}}{V}[/tex]
∴
[tex]\frac{V}{N*1.66*10^{-24}} = \frac{1}{ D}[/tex]
⇒ λ = [tex]\frac{1}{\sqrt{2}\pi d^{2}D }[/tex]
⇒ λ = [tex]\frac{1.66*10^{-24}}{\sqrt{2}\pi (100*10^{-12})^{2}*1 }[/tex]
⇒ λ = [tex]0.0000373631 m[/tex]
