At a certain temperature,the r.m.s. velocity | vedclass

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(C) The formula for $r.m.s.$ velocity is given by ${v_{rms}} = \sqrt{\frac{3RT}{M}}$.Since the temperature $T$ is constant,we have ${v_{rms}} \propto

Vedclass · Accepted Answer

$1600$

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(C) The formula for $r.m.s.$ velocity is given by ${v_{rms}} = \sqrt{\frac{3RT}{M}}$.Since the temperature $T$ is constant,we have ${v_{rms}} \propto \frac{1}{\sqrt{M}}$.Therefore,the ratio of the $r.m.s.$ velocities of ${O_2}$ and ${H_2}$ is given by:$\frac{{{{({v_{rms}})}_{{O_2}}}}}{{{{({v_{rms}})}_{{H_2}}}}} = \sqrt{\frac{{{M_{{H_2}}}}}{{{M_{{O_2}}}}}}$Given that ${M_{{O_2}}} = 32$ and ${M_{{H_2}}} = 2$,we substitute the values:$\frac{{400}}{{{{({v_{rms}})}_{{H_2}}}}} = \sqrt{\frac{2}{32}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$Solving for ${({v_{rms}})_{{H_2}}}$,we get:${({v_{rms}})_{{H_2}}} = 400 	imes 4 = 1600\, m/s$.

At a certain temperature,the $r.m.s.$ velocity for ${O_2}$ is $400\, m/sec.$ At the same temperature,the $r.m.s.$ velocity for ${H_2}$ molecules will be ....... $m/sec$.

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