Both neon `[ M_(Ne) = 20 xx 10^(-3) kg]` and helium `[M_(He) = 4 xx 10^(-3) kg]` are monoatomic gases and can be assumed to be ideal gases. The fundamental frequency of a tube (open at both ends ) of neon is `300 Hz at 270 K (R = ( 25//3) J//K mol)`
The length of the tube is

Options

A. `(5)/(12) m`
B. `(sqrt(3))/(12) m`
C. `( 5 sqrt(3))/(12) m`
D. ` ( 5 sqrt(3)) m`

Answer

C

Explanation

Fundamental frequency
`n_(Ne) = (1)/( 2L) sqrt((gamma RT)/( M_(Ne)))`
`n_(Ne) = 300 Hz , M_(Ne) = 20 xx 10^(-3) kg`
`gamma = (5)/(3) , R = (20)/(3) J//mol K`
`T = 270 K`
`L = (1)/( 2 xx 300) sqrt((5/3 xx 25/3 xx 270)/(20 xx 10^(-3)))`
` = ( 250 sqrt(3))/( 2 xx 300) = ( 5 sqrt(3))/(12) m`