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Question
Two molecules of a gas have speeds of 9 × 10 6 ms−1 and 1 × 106 ms−1, respectively. What is the root mean square speed of these molecules?
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Solution
For n-molecules, we know that
`v_(rms) = sqrt((v_1^2 + v_2^2 + v_3^2 + ...... + v_n^2)/n` .....`[(v_(rms) = "root mean"),("square velocity")]`
Where v1, v2, v3 ....... vn are individual velocities of n-molecules of the gas.
For two molecules,
`v_(rms) = sqrt((v_1^2 + v_2^2)/2` ......[v1, v2, v3 ....... vn are individual velocity]
Given, `v_1 = 9 xx 10^6` m/s
And `v_2 = 1 xx 10^6` m/s
∴ `v_(rms) = sqrt(((9 xx 10^6)^2 + (1 xx 10^6)^2)/2`
= `sqrt((81 xx 10^12 + 1 xx 10^12)/2`
= `sqrt(((81 + 1) xx 10^12)/2`
= `sqrt((82 xx 10^12)/2`
= `sqrt(41) xx 10^6` m/s
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