Question

The rms velocity of molecules of a gas of density $4~\text{kg m}^{-3}$ and pressure $1.2 \times 10^{5}~\text{N m}^{-2}$ is

• A. $300~ms^{-1}$
• B. $900~ms^{-1}$
• C. $120~ms^{-1}$
• D. $600~ms^{-1}$

Hint:

$V_{rms}$ is inversely proportional to the square root of density.

Answer 1

The Correct Option is A

Step 1: Formula
The root mean square velocity is $v_{rms} = \sqrt{\frac{3P}{d}}$.
Step 2: Substitution
$v_{rms} = \sqrt{\frac{3 \times 1.2 \times 10^{5}}{4}}$.
Step 3: Calculation
$v_{rms} = \sqrt{0.9 \times 10^{5}} = \sqrt{90000} = 300~ms^{-1}$.
Final Answer: (a)