Question

What would be the most probable velocity for one Oxygen molecule at 300 K?

(a) 612 m/s

(b) 714 m/s

(c) 798 m/s

(d) 821 m/s

I got this question in an interview for internship.

This interesting question is from Maxwell Boltzmann Statistics topic in section Quantum Physics of Engineering Physics I

Answer 1

Right option is (b) 714 m/s

For explanation: Mass of one Oxygen molecule = 32 g/mol

= 32 X 10^-3/6.022 X 10^23

= 5.31 X 10^-26 Kg

Now,\(V_p = \sqrt{\frac{2kT}{M}}\)

Here, T = 300 K, k = 1.98 X 10^23 and M = 32

Therefore, \(V_p = \sqrt{\frac{2X 1.98X 30}{5.31}} \) X 10^4

= 714 m/s.