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At what temperature is the rms velocity ...

At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at `47^(@)C`?

A

`80 K`

B

`-73 K`

C

`3 K `

D

`20 K`

Text Solution

Verified by Experts

The correct Answer is:
D
The rms velocity of the molecules of a gas of molecular weight M at temperature T is given by
`C_(ms)=sqrt((3RT)/(M))`.
Let `M_O" and "M_H` be molecular weights of oxygen and hydrogen `T_O" and "T_H` be the corresponding kelvin temperatures at which `C_(ms)` is same for both gases.
`C_(ms(o))=C_(ms(H))`
`sqrt((3RT_(o))/(M_(o)))=sqrt((3RT_(H))/(M_(H)))`
Hence, `(T_o)/(M_o)=(T_H)/(M_H)`
Given `T_o=273+47=320K" and "M_o=32, M_H=2" ":. T_H= (2)/(32)xx320= 20K`.
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