Question

The root mean square speed of smoke particles each of mass $5 \times 10^{-17}\, kg$ in their Brownian motion in air at $N.T.P$ is

• A. $3 \times 10^{-2} \,m \,s^{-1}$
• B. $1.5 \times 10^{-2} \,m \,s^{-1}$
• C. $3 \times 10^{-3} \,m \,s^{-1}$
• D. $1.5 \times 10^{-3} \,m \,s^{-1}$

Answer 1

Answer: (B)

According to Kinetic theory,
average $K.E.$ of a gas molecule $= \frac{1}{2} mv^{2}_{rms} = \frac{3}{2}k_{B}T$
$\therefore \quad v_{rms} = \sqrt{\frac{3k_{B }T}{m}} = \sqrt{\frac{3\,\times\,1.38\,\times \,10^{-23}\,\times \,273}{5\,\times \,10^{-17}}}$
$= 1.5\,\times \,10^{-2}\,m\,s^{-1}$