Collision Between Molecules

Question:
Consider N₂ molecules at 1 atm and 300 K. Assume that the molecules are spherical with diameter d=0.385 nm.
a) Calculate the number of collisions per unit time per unit volume.
b) What is the average time between collisions?
c) Assume that N₂ is a harmonic oscillator with ν = 2360 cm⁻¹ . How many oscillations the molecule makes during the time between collisions?
d) Assume that the rotational energy per molecule is k_BT and the equilibrium bond length is 0.1094 nm. How many rotations does the molecule make during the time between the collisions?

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