The mean free path for the molecules of a gas is approximately given by 1/ησ, where η is the number density and σ is the collision cross section. The mean free path for air molecules at room conditions is approximately
A. 10−4 m
B. 10−7 m
C. 10−10 m
D. 10−13 m
E. 10−16 m
(GR9677 #16)
Mean free path = 1/ησ
Number density, η = N/V
Cross section area, σ = πr2
For Ideal Gas: PV = NkT
1/ησ = V / Nπr2 = NkT / PNπr2 = kT / Pπr2
k = 1.38 × 10−23 Joule/K
Radius of atom is in order of Angstrom: 10−10 m
P (STP) = 1 atm = 105 Newton/meter2
T (STP) = 0 °C = 32 °F = 273.15 K ≈ 2 × 102 K
kT / Pπr2 = (1.38 × 10−23 × 2 ×102) / (π ×105 × 10−20)
= (1.38 × 2 / π) 10−23+2−5+20 ≈ 10−7
Answer: B
