The root mean square speed of molecules of ni | vedclass

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(A) The root mean square speed $(V_{rms})$ of gas molecules is given by the formula: $V_{rms} = \sqrt{\frac{3 k_{B} T}{m}}$.Given:Temperature $T = 27^

Vedclass · Accepted Answer

$523$

Vedclass · Answer

(A) The root mean square speed $(V_{rms})$ of gas molecules is given by the formula: $V_{rms} = \sqrt{\frac{3 k_{B} T}{m}}$.Given:Temperature $T = 27^{\circ} C = 27 + 273 = 300 \, K$.Mass of a nitrogen molecule $m = 4.6 	imes 10^{-26} \, kg$.Boltzmann constant $k_{B} = 1.4 	imes 10^{-23} \, J K^{-1}$.Substituting the values into the formula:$V_{rms} = \sqrt{\frac{3 	imes 1.4 	imes 10^{-23} 	imes 300}{4.6 	imes 10^{-26}}}$$V_{rms} = \sqrt{\frac{1260 	imes 10^{-23}}{4.6 	imes 10^{-26}}}$$V_{rms} = \sqrt{273.91 	imes 10^{3}} \approx \sqrt{273910} \approx 523.36 \, m/s$.Thus,the approximate speed is $523 \, m/s$.

The root mean square speed of molecules of nitrogen gas at $27^{\circ} C$ is approximately $.......m/s$. (Given: mass of a nitrogen molecule $= 4.6 \times 10^{-26} \, kg$ and Boltzmann constant $k_{B} = 1.4 \times 10^{-23} \, J K^{-1}$)

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