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  • Calculate the root mean square speed of smoke particles of mass <img alt="5 \times 10^{-17} \mathrm{~kg}" src="https://entrancecorner.oncodecogs.com/gif.latex?5%20%5Ctimes%2010%5E%7B-17%7D%20%5Cmat

Calculate the root mean square speed of smoke particles of mass 5 \times 10^{-17} \mathrm{~kg} in Brownian motion in air at NTP. Boltzmann constant \mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}

Option: 1

\quad 1.5 \mathrm{~cm} / \mathrm{s}


Option: 2

\quad 2.2 \mathrm{~cm} / \mathrm{s}


Option: 3

2.3 \mathrm{~cm} / \mathrm{s}


Option: 4

4.4 \mathrm{~cm} / \mathrm{s}


Answers (1)

best_answer

\mathrm{\quad P V=\frac{1}{3} m V_{\text {rms }}^{2}=\frac{m}{M} R T}
\mathrm{\Rightarrow \quad \mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{3(\mathrm{NK}) \mathrm{T}}{\mathrm{N} \mu}}}
\mathrm{=\sqrt{\frac{3 \mathrm{kT}}{\mu}}}

where \mathrm{\mu=} mass of one molecule.
\mathrm{\therefore \quad \mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \times 1.38 \times 10^{-23} \times 273}{5 \times 10^{-17}}}}
\mathrm{ =15 \times 10^{-3} \mathrm{~m} / \mathrm{s}=1.5 \mathrm{~cm} / \mathrm{s}}
 

Posted by

Divya Prakash Singh

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