First slide

Rms speed

Question

The rms speed of particle of mass $5 x 10^{- 17}$ kg. in their random motion in air at NTP will be (Boltzmann's constant $K = 1.38 x l 0^{- 23} J / K$ )

Easy

A

$15 \times 10 m / s$
B

$15 \times 10^{- 3} m / s$
C

$10 \times 10^{- 2} m / s$
D

$1.5 \times 10^{2} m / s$

Solution

Given
Mass of the particle m = $5 \times 10^{- 17} kg$
Absolute temperature = 273 K
The rms speed of the particle is given by
$v_{rms} = \sqrt{\frac{3 KT}{m}} = \sqrt{\frac{3 \times 1.38 \times 10^{- 23} \times 273}{5 \times 10^{- 17}}}$
= $\sqrt{226 \times 10^{- 6}} = 15 \times 10^{- 3}$ m/s

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