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Root mean square speed of a gas is 5 ms^...

Root mean square speed of a gas is `5 ms^(-1)` If some molecules out of 10 molecules in all are moving with `7ms^(-1)` and rest all the molecules moving with `3 m sec^(-1)` then number of molecules moving with higher speed is ____________.

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The correct Answer is:
4
Let the no. of molecules moving with
Speed of `3 ms^(-1)` be `n_(1)`, , Speed of `7 ms^(-1)` be `n_(2)`
So, `n_(1) + n_(2) = 10, " Also, " C_(rm s) = sqrt((n_(1) C_(1)^(2) + n_(2) C_(2)^(2))/(n_(1) + n_(2))) = 5`
`9n_(1) + 49n_(2) = 25n_(1) + 25n_(2)`
`rArr n_(1) = (3)/(2) n_(2) or, n_(1) = 6 " &" n_(2) = 4`
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