In the two vessels of same volume, atomic hydrogen and helium at pressure 1 atm and 2 atm are filled. If temperature of both the sample is same then average speed of hydrogen atoms `ltC_(H)lt` will be related to that of helium `ltC_(He)gt` as

Options

A. `ltC_Hgt=sqrt2ltC_"He"gt`
B. `ltC_Hgt =ltC_"He"gt`
C. `ltC_Hgt=2ltC_"He"gt`
D. `ltC_Hgt = (ltC_"He"gt)/2`

Answer

C

Explanation

`v_(avg)=sqrt((8RT)/(piM)) implies v_(avg) prop (1)/(sqrtM)`
`implies ( lt C_H gt)/(lt C_(H_e) gt)= sqrt((M_(H_e))/(M_H))=sqrt(4/1)=2`
`implies lt C_H gt =2 lt C_(H_e) gt`.