For a given gas,the velocities of 5 molecules | vedclass

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(D) The root mean square $(rms)$ velocity is defined as the square root of the mean of the squares of the individual velocities.Formula: $\upsilon_{rm

Vedclass · Accepted Answer

$4.24$

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(D) The root mean square $(rms)$ velocity is defined as the square root of the mean of the squares of the individual velocities.Formula: $\upsilon_{rms} = \sqrt{\frac{\upsilon_1^2 + \upsilon_2^2 + \upsilon_3^2 + \upsilon_4^2 + \upsilon_5^2}{N}}$Given velocities: $\upsilon_1 = 2, \upsilon_2 = 3, \upsilon_3 = 4, \upsilon_4 = 5, \upsilon_5 = 6$ and $N = 5$.Calculation: $\upsilon_{rms} = \sqrt{\frac{2^2 + 3^2 + 4^2 + 5^2 + 6^2}{5}}$$\upsilon_{rms} = \sqrt{\frac{4 + 9 + 16 + 25 + 36}{5}}$$\upsilon_{rms} = \sqrt{\frac{90}{5}}$$\upsilon_{rms} = \sqrt{18}$$\upsilon_{rms} \approx 4.24$

For a given gas,the velocities of $5$ molecules are $2, 3, 4, 5,$ and $6$. What is the $rms$ velocity?

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