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Q.

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 ]

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a

$15 {mms}^{- 1}$

b

$36 {mms}^{- 1}$

c

$60 {mms}^{- 1}$

d

$12 {mms}^{- 1}$

answer is C.

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Detailed Solution

$\begin{aligned} v_{rms} = \sqrt{\frac{3 kT}{m}} = \sqrt{\frac{3 \times 1 .38 \times 10^{- 23} \times 293}{5 \times 10^{- 17}}} \\ \approx 15 mm / s \end{aligned}$

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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 ]