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Physics Question on speed and velocity

The root mean square speed of smoke particles of mass 5 × 10-17 in their Brownian motion in air at NTP is approximately. [Given k = 1.38 × 10-23 JK-1]

A

60 mm s-1

B

12 mm s-1

C

15 mm s-1

D

36 mm s-1

Answer

15 mm s-1

Explanation

Solution

At NTP, T=298 K
⇒vrms=3RTM\sqrt\frac{3RT}{M}
=3kNA×2985×10−17×NA=\sqrt{\frac{3kN_A×298}{5×10^{−17}×N_A}}
≃15 mm/s
So, the correct option is (C): 15 mm s-1