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Asked by Urvashi Last Modified
Answer 
Harshit Bhardwaj
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:
Where,
R is the universal gas constant = 8.314 J mole–1 K–1
= 508.26 m/s
The mean free path (l) is given by the relation:
Where,
k is the Boltzmann constant = 1.38 × 10–23 kg m2 s–2K–1
= 1.11 × 10–7 m
Collision frequency 
= 4.58 × 109 s–1
Collision time is given as:
= 3.93 × 10–13 s
Time taken between successive collisions:
= 2.18 × 10–10 s
∴ 
Hence, the time taken between successive collisions is 500 times the time taken for a collision.
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