Question

At 300$K$, the number of molecules possessing most probable velocity are 100. At 400$K$ the number of such molecules will be:

• A. $65$
• B. $100$
• C. $110$
• D. $120$

Answer 1

The correct option is A $65$

From Maxwell Boltzmann's distribution,

$f\left(c\right)=4\pi c^2(\frac{m}{2\pi k_{B}T}{)}^{3/2}{e}^{\frac{m{c}^2}{2k_{B}T}}$

here $f\left(c\right)$ is the form of function defines the distribution of the gas molecules moving at different speeds.

so, no of particle at 400K moving with most probable speed /no of particle at 300K moving with most probable speed = $(300/400{)}^{3/2}$

or, no of particle at 400K moving with most probable speed $=(300/400{)}^{3/2}\times 100=64.9565$