Mean free path = 1.11 × 10–7 m
Collision frequency = 4.58 × 109 s–1
Successive collision time ≈ 500 × (Collision time)
Pressure inside the cylinder containing nitrogen,
P = 2.0 atm
= 2.026 × 105 Pa
Temperature inside the cylinder, T = 17°C =290 K
Radius of a nitrogen molecule, r = 1.0 Å
= 1 × 1010 m
Diameter, d = 2 × 1 × 1010 = 2 × 1010 m
Molecular mass of nitrogen, M = 28.0 g
= 28 × 10–3 kg
The root mean square speed of nitrogen is given by the relation,
Collision frequency =
= 508.26 / (1.11 × 10-7)
= 4.58 × 109 s-1
Collision time is given as,
T =
=
= 3.93 × 10-13 s
Time taken between successive collisions,
T ' = l / vrms
= 1.11 × 10-7 / 508.26
= 2.18 × 10-10 s
Therefore,
Hence, the time taken between successive collisions is 500 times the time taken for a collision.