The root mean square speed of smoke particles of mass $5 \times 10^{- 17} kg$ in their Brownian motion in air at NTP is approximately.
[Given $k = 1.38 \times 10^{- 23} J K^{- 1}$ ]

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 J K - 1 ]

TestHub · Accepted Answer

According to Kinetic theory,
Average kinetic energy of a gas molecule $= \frac{1}{2} m v_{r m s}^{2} = \frac{3}{2} k T$
Thus, $v_{rms} = \sqrt{\frac{3 k T}{m}}$
At NTP, $T = 293 K$
Putting the values, we have
$= \sqrt{\frac{3 \times 1.38 \times 10^{- 23} \times 293}{5 \times 10^{- 17}}}$
$\approx 15 mm s^{- 1}$

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