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 ]

Quantrex Academy · Accepted Answer

Correct answer: C. 15mm s ^ - 1

According to Kinetic theory,
Average kinetic energy of a gas molecule $= \dfrac{1}{2}m{v}_{rms}^{2} = \dfrac{3}{2}kT$
Thus, ${v}_{rms} = \sqrt{\dfrac{3kT}{m}}$
At NTP, $T = 293K$
Putting the values, we have
$= \sqrt{\dfrac{3 \times 1 . 38 \times {10}^{- 23} \times 293}{5 \times {10}^{- 17}}}$
$\approx 15mm{s}^{- 1}$

The root mean square speed of smoke particles of mass 5 × 10 ^ - 17...

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