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. 4 K
C. `273^(@)C`
D. `100^(@)C`

Answer

C

Explanation

As, `(c_(He)/c_(H))=sqrt((gammarho)/(rho))=sqrt((1)/(4))=(1)/(2)" or" (c_(He))t=(c_(He))_(0)sqrt((T)/(T_(0)))`
`therefore" " (c_(He))_(t)/(c_(H))_(0)=(c_(He))_(0)/(c_(H))_(0)sqrt((T)/(t))=(5)/(7)`
`"or" " " T~~2T_(0)=2xx273=546^(@)K=273^(@)C`