Question

Interstellar space has an average temperature of about 10 K and an average density of hydrogen atoms of about one hydrogen atom per cubic meter. Calculate the mean free path of hydrogen atoms in interstellar space. Take d = 100 pm for a hydrogen atom.

Answer 1

Answer:

The mean free path is $0.0000373631 m$

Explanation:

The formula for mean free path is :

λ = $\frac{V}{\sqrt{2}\pi d^{2}N }$

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 $D$ = $\frac{mass}{volume}$ = $\frac{M}{V}$ ;

mass of the gas = (number of molecules)$*$(mass of one molecule) ;

as it's atomic hydrogen

$M = N*m \\m=1.66*10^{-24}\\M=N*1.66*10^{-24}$

∴  

$D$ = $\frac{N*1.66*10^{-24}}{V}$

∴

$\frac{V}{N*1.66*10^{-24}} = \frac{1}{ D}$

⇒ λ = $\frac{1}{\sqrt{2}\pi d^{2}D }$

⇒ λ = $\frac{1.66*10^{-24}}{\sqrt{2}\pi (100*10^{-12})^{2}*1 }$

⇒ λ = $0.0000373631 m$