If the mean free path of O₂ molecules at STP is 6.33X10⁻⁸ m , then their collision frequency is 0.49 × [tex]10^{-33}[/tex] per second .
Calculation ,
The expression for mean free path is given as ,
lamda = [tex]v_{rms}[/tex] × f
where lamda is mean free path = 6.33X10⁻⁸ m
f is collision frequency = ?
and [tex]v_{rms}[/tex] root mean square velocity.
[tex]v_{rms}[/tex] = √3RT/M = √ 3 × 8.314 × 273 / 5.314 × [tex]10^{-23}[/tex] = 12.8 × [tex]10^{25}[/tex] m/s
putting the value of lamda and [tex]v_{rms}[/tex] in equation ( i ) we get ,
6.33X10⁻⁸ m = 12.8 × [tex]10^{25}[/tex] m/s × f
f = 6.33X10⁻⁸ m / 12.8× [tex]10^{25}[/tex] m/s = 0.49 × [tex]10^{-33}[/tex] per second
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