Question

The root mean square speed of smoke particles each of mass 5 × 10–17 kg in their Brownian motion in air at N.T.P is

• A. 3 × 10–2 m s–1
• B. 1.5 × 10–2 m s–1
• C. 3 × 10–3 m s–1
• D. 1.5 × 10–3 m s–1

Answer 1

Answer: (B)

1.5 × 10–2 m s–1

Answer 2

According of Kinetic theory, average K.E. of a gas molecule

$\frac{1}{2}M{v^{2}}_{rms} = \frac{3}{2}k_{B}T$

$\therefore V_{rms} = \sqrt{\frac{3k_{B}T}{m}} = \sqrt{\frac{3 \times 1.38 \times 10^{- 23} \times 273}{5 \times 10^{- 17}}}$

$= 1.5 \times 10^{- 2}ms^{- 1}$