The root mean square speed of smoke particles of mass 5 × 10-17 kg in their Brownian motion in air at NTP is approximately. [Given .k =1.38 × 10-23 JK -1]

Question

The root mean square speed of smoke particles of mass 5 × 10-17 kg in their Brownian motion in air at NTP is approximately. [Given .k =1.38 × 10-23 JK -1] (A) 60 mm s -1 (B) 12 mm s -1 (C) 15 mm s -1 (D) 36 mm s -1

Tardigrade Admin · Accepted Answer

V rms =√(3 kT / m )=√(3 × 1.38 × 10-23 × 293/5 × 10-17) ≈ 15 mm / s

Q. The root mean square speed of smoke particles of mass $5 \times 1 0^{- 17} k g$ in their Brownian motion in air at NTP is approximately.
[Given $k = 1.38 \times 1 0^{- 23} J K^{- 1}]$

$60 mm s^{- 1}$

$12 mm s^{- 1}$

$15 mm s^{- 1}$

$36 mm s^{- 1}$

$V_{r m s} = \frac{3 k T}{m} = \frac{3 \times 1.38 \times 1 0 ^{- 23} \times 293}{5 \times 1 0 ^{- 17}}$
$\approx 15 mm / s$

Q. The root mean square speed of smoke particles of mass 5×10−17kg in their Brownian motion in air at NTP is approximately. [Given k=1.38×10−23JK−1]

60mms−1

12mms−1

15mms−1

36mms−1