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 kBT and the equilibrium bond length is 0.1094 nm. How many rotations does the molecule make during the time between the collisions?

Solution:
a) The number of collisions of molecules with the same type per unit time per unit volume is given by,

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