First slide

Rms speed

Question

An assembly of smoke particles in air at NTP is under consideration. If the mass of each particle is $5 x l 0^{- 17} kg$ , then the rms speed is
(Given: k = 1.38 ${×19}^{- 23} {JK}^{- 1}$ )

Easy

A

$1.5 cm s^{- 1}$
B

$1.5 mm s^{- 1}$
C

1.5 ${ms}^{- 1}$
D

$1.5 km s^{- 1}$

Solution

$\frac{1}{2} {mC}^{2} = \frac{3}{2} kT, C = \sqrt{\frac{3 kT}{m}}$
= $\sqrt{\frac{3 \times 1.38 \times 10^{- 23} \times 273}{5 \times 10^{- 17}}}$
= 15 $\times 10^{- 3} {ms}^{- 1} = 1.5 {cms}^{- 1}$

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