Two gases - argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to :

Question

Two gases - argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to : (A) 4.67 (B) 2.3 (C) 1.83 (D) 1.09

Tardigrade Admin · Accepted Answer

λ = (1/√2π nvd2) τ = (λ/v) = (1/√2π nvd2v)= (1/√2π nvd2)√(M/3RT) (τ1/τ2) = √(M1/M2) (d22/d21) = √(40/140) ((0.1)2/(0.07)2) = 1.09

Q. Two gases - argon (atomic radius $0.07 nm$ , atomic weight $40$ ) and xenon (atomic radius $0.1 nm$ , atomic weight $140$ ) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to :

$4.67$

$2.3$

$1.83$

$1.09$

$λ = \frac{1}{2 π n _{v} d ^{2}}$
$τ = \frac{λ}{v} = \frac{1}{2 π n _{v} d ^{2} v} = \frac{1}{2 π n _{v} d ^{2}} \frac{M}{3 RT}$
$\frac{τ _{1}}{τ _{2}} = \frac{M _{1}}{M _{2}} \frac{d _{2}^{2}}{d _{1}^{2}}$
$= \frac{40}{140} \frac{( 0.1 ) ^{2}}{( 0.07 ) ^{2}}$
$= 1.09$

Q. Two gases - argon (atomic radius 0.07nm, atomic weight 40) and xenon (atomic radius 0.1nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to :

4.67

2.3

1.83

1.09