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

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

Tardigrade Admin · Accepted Answer

According to Kinetic theory, average K.E. of a gas molecule = (1/2) mv2rms = (3/2)kBT ∴ vrms = √(3kB T/m) = √(3 × 1.38 × 10-23 × 273/5 × 10-17) = 1.5 × 10-2 m s-1

Q. The root mean square speed of smoke particles each of mass $5 \times 1 0^{- 17} k g$ in their Brownian motion in air at $N . T . P$ is

$3 \times 1 0^{- 2} m s^{- 1}$

$1.5 \times 1 0^{- 2} m s^{- 1}$

$3 \times 1 0^{- 3} m s^{- 1}$

$1.5 \times 1 0^{- 3} m s^{- 1}$

According to Kinetic theory,
average $K . E .$ of a gas molecule $= \frac{1}{2} m v_{r m s}^{2} = \frac{3}{2} k_{B} T$
$∴ v_{r m s} = \frac{3 k _{B} T}{m} = \frac{3 \times 1.38 \times 1 0 ^{- 23} \times 273}{5 \times 1 0 ^{- 17}}$
$= 1.5 \times 1 0^{- 2} m s^{- 1}$

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

3×10−2ms−1

1.5×10−2ms−1

3×10−3ms−1

1.5×10−3ms−1