At what temperature is the root mean square velocity of gaseous hydrogen molecule equal to that of oxygen?

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Text Solution

`20 K``80 K``-73 K``3 K`

Answer : A

Solution : For oxygen `V_(O_2) = sqrt((3RT_(O_2))/(M_(O_2)))` and <br> For hydrogen, `v_(H_2) = sqrt(3R(T_(H_2))/(M_(H_2)))` <br> According to problem `= sqrt((3RT_(O_2))/(M_(O_2))) = sqrt(3R(T_(H_2))/(M_(H_2)))` <br> `implies (T_(O_2))/(M_(O_2)) = (T_(H_2))/(M_(H_2)) implies (47+273)/(32) = (T_(H_2))/(M_(H_2))` <br> `implies T_(H_2) = (320)/(32)xx2 = 20K`.