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. `100^(@)`
B. `273^(@)C`
C. 173 K
D. `0^(@)C`

Answer

D

Explanation

As `(V_(He))/(V_(H2)) = (sqrt((3RT_(He))/M_(He)))/(sqrt((3RT_(H2))/(M_(H2))))`
` = sqrt((M_(H2))/(M_(He)) .(T_(He))/(T_(H2)))`
` = sqrt((2)/(4) xx (T_(He))/(273))`
` (5)/(7) = sqrt((T_(He))/(2 xx 273))`
` rArr T_(He) = (25 xx 27 xx 2)/(49) ~~ 278K`
`= 5^(@) C ~~ 0^(@)C`