The root mean square speed of molecules of nitrogen gas at $27^{\circ} \mathrm{C}$ is approximately

Question

The root mean square speed of molecules of nitrogen gas at $27^{\circ} \mathrm{C}$ is approximately ( given mass of a nitrogen molecule $=4.6 	imes 10^{-26} \mathrm{~kg}$ and take Boltzmann constant $K_B=1.4 	imes 10^{-13} \mathrm{JK}^{-1}$ )

Professor PC Thomas Classes · Answer

$v_{	ext{rms}} = \sqrt{\frac{3K_B T}{m}} = \sqrt{\frac{3 	imes 1.4	imes 10^{-23} 	imes 300}{4.6	imes 10^{-26}}} \approx 523$ m/s.