Consider an ideal gas at pressure p, volume V and temperature T. The mean free path for molecules of the gas is L. If the radius of gas molecules, as well as pressure, volume and temperature of the gas are doubled, then the mean free path will be

Options

A. `(5L)/(2)`
B. `(L)/(4)`
C. `(L)/(8)`
D. 2L

Answer

B

Explanation

Given initial values of pressure, volume temperature, radius of molecule of gas and mean free path are Pp,V,T, r and L respectively.
`:.` Mean free path,
`lamda=(2sqrt2)/(pir^(2))(RT)/(Np)`
`:.L=(2sqrt2)/(pir^(2))(RT)/(Np)" "......(i)`
According to question if the radius of gas molecules, as well as pressure volume and temperature of gas are doubled then
`lamda'=(2sqrt2R.2T)/(pixx4r^(2)xxNxx2p)`
`=(1)/(4).(2sqrt2RT)/(pir^(2)Np)=(L)/(4)` (From Eq. (i))
Hence, the mean free path will be `(L)/(4)`.