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(A) The root mean square velocity $(v_{rms})$ is given by the formula: $v_{rms} = \sqrt{\frac{v_1^2 + v_2^2 + v_3^2 + v_4^2 + v_5^2}{n}}$.Substituting

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$\sqrt{11} : 3$

Vedclass · Answer

(A) The root mean square velocity $(v_{rms})$ is given by the formula: $v_{rms} = \sqrt{\frac{v_1^2 + v_2^2 + v_3^2 + v_4^2 + v_5^2}{n}}$.Substituting the given values: $v_{rms} = \sqrt{\frac{1^2 + 2^2 + 3^2 + 4^2 + 5^2}{5}} = \sqrt{\frac{1 + 4 + 9 + 16 + 25}{5}} = \sqrt{\frac{55}{5}} = \sqrt{11} \ km/s$.The average velocity $(v_{av})$ is given by the formula: $v_{av} = \frac{v_1 + v_2 + v_3 + v_4 + v_5}{n}$.Substituting the given values: $v_{av} = \frac{1 + 2 + 3 + 4 + 5}{5} = \frac{15}{5} = 3 \ km/s$.The ratio of $v_{rms}$ to $v_{av}$ is $\frac{\sqrt{11}}{3}$,which is $\sqrt{11} : 3$.

The respective speeds of the molecules are $1, 2, 3, 4$ and $5 \ km/sec$. The ratio of their $r.m.s.$ velocity and the average velocity will be

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