Question

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 $\left.k =1.38 \times 10^{-23} \,JK ^{-1}\right]$

• A. $60 \,mm \,s ^{-1}$
• B. $12 \, mm \, s ^{-1}$
• C. $15 \,mm \,s ^{-1}$
• D. $36 \,mm \, s ^{-1}$

Answer 1

Answer: (C)

$ V _{ rms }=\sqrt{\frac{3 kT }{ m }}=\sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 293}{5 \times 10^{-17}}} $
$ \approx 15\, mm / s$