Question

Which of the following options may be the correct estimate of the mean free path of gas particles? [n: Number of gas particle per unit volume, d: diameter]

विकल्प

• λ = `1/("d"^2"n"^2)`

• λ = `("n"^2"d")/sqrt2`

• λ = `("nd"^2)/sqrt2`

• λ = `1/(sqrt2"nd"^2)`

Answer 1

`bb(λ = 1/(sqrt2"nd"^2))`

Explanation:

The mean free path is defined as the average distance a gas particle travels before colliding.

∴ n = [M⁰ L^–3 T⁰] d = [M⁰ L¹ T⁰]

∴ `1/(sqrt2"nd"^2) = 1/(["M"^0 "L"^(–3) "T"^0 ] ["M"^0 "L"^1 "T"^0])`

=  [M⁰L¹T⁰]