A vessel is partitioned in two equal halves by a fixed diathermic separator. Two different ideal gases ae filled in left (L) and right (R) halves the rms speed of the molecules in L part is equal to the mean speed of moleucles in the R equal to the ratio of the mass of a molecules in L part to that of a molecules in R part is

Options

A. `sqrt((3)/(2))`
B. `sqrt(pi//4)`
C. ` sqrt(2//3)`
D. ` 3pi//8`

Answer

D

Explanation

Root means square velocity of molecule in left part
`V_(n ns) =sqrt((3KT)/(m_(L)))`
Mean or average speed of moleucles in right part
`V_(av)=sqrt((8KT)/(pim_(k)))`
According to problem `sqrt((3KT)/(m_(L)))=sqrt((8)/(pi)(KT)/(m_(R)))`
` rArr " " (3)/(m_(L))=(8)/(pim_(R))`
`rArr" " (m_(L))/(m_(R))=(3pi)/(8)`