The root mean square velocity of the molecules in a sample of helium is `5//7th` that of the molecules in a sample of hydrogen. If the temperature of hydrogen sample is `0^(@)C`, then the temperature of the helium sample is about

Options

A. `0^@C`
B. `0K`
C. `273^@C`
D. `100^@C`

Answer

A

Explanation

`v_(rms)=sqrt((3RT)/(M)) implies v_(rms) prop sqrt(T/M)`
`(v_(He))/(v_(H_2))=5/7 implies sqrt((T_(He))/(M_(He))xx(M_(H_2))/(T_(H_2)))=5/7`
`implies T_(He)=(25)/(49)xx4/2 xx 273 ~~ 273 K ~~ 0^@C`.