The root mean square speed of smoke particles | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The root mean square speed $(V_{	ext{rms}})$ of a particle is given by the formula: $V_{	ext{rms}} = \sqrt{\frac{3kT}{m}}$.Given:Mass of particl

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(C) The root mean square speed $(V_{	ext{rms}})$ of a particle is given by the formula: $V_{	ext{rms}} = \sqrt{\frac{3kT}{m}}$.Given:Mass of particle $(m)$ = $5 	imes 10^{-17} \, kg$Boltzmann constant $(k)$ = $1.38 	imes 10^{-23} \, J \, K^{-1}$Temperature at $NTP$ $(T)$ = $293 \, K$Substituting the values:$V_{	ext{rms}} = \sqrt{\frac{3 	imes 1.38 	imes 10^{-23} 	imes 293}{5 	imes 10^{-17}}}$$V_{	ext{rms}} = \sqrt{\frac{1213.02 	imes 10^{-23}}{5 	imes 10^{-17}}}$$V_{	ext{rms}} = \sqrt{242.604 	imes 10^{-6}}$$V_{	ext{rms}} \approx 15.57 	imes 10^{-3} \, m/s$Converting to $mm/s$ $(1 \, m/s = 1000 \, mm/s)$:$V_{	ext{rms}} \approx 15.57 \, mm/s \approx 15 \, mm/s$.

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 $....... \, mm \, s^{-1}$. [Given $k = 1.38 \times 10^{-23} \, J \, K^{-1}$ and $T = 293 \, K$]

Similar Questions

The $rms$ speed of helium gas at $27\,^{\circ}C$ and $1\,atm$ pressure is $900\,ms^{-1}$. Then the $rms$ speed of helium molecules at temperature $27\,^{\circ}C$ and $2\,atm$ pressure is ...... $m/s$.

The velocity of the molecules of a gas at temperature $120\,K$ is $v$. At what temperature in $K$ will the velocity be $2v$?

At what temperature $(K)$ will the $r.m.s.$ velocity of hydrogen gas be equal to the escape velocity from the Earth?

The number of molecules in a closed container is doubled. What will be the effect on $v_{rms}$?

The r.m.s. speed of hydrogen at $S.T.P.$ is $u \text{ m/s}$. If the gas is heated at constant pressure till its volume becomes three times, the final temperature of the gas and the r.m.s. speed are respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module