If m represents the mass of each molecule of a gas and T, its absolute temperature, then the root mean square velocity of the gaseous molecule is proportional to

Options

A. mT
B. `m ^(1//2) T ^(1//2)`
C. `m ^(-1//2) T`
D. `m ^(-1//2) T ^(1//2)`

Answer

D

Explanation

We know that,
Thermal equilibrium and kinetic interpretation of temperature
`bar v ^(2) = ( 3RT)/(M)`
`v _(rms) = sqrt (( 3 RT)/(M ))`
`So, v _(rms ) prop sqrtT`
and `v _(rms) prop (1)/(sqrtm)`
The root mean square speed of the molecules of a gas is directly proportional to the square root of the absolute temperature of the gas and inversely proportional to the square root of the mass of molecules of the gas.
`v _(rms) = m ^(-1//2) xx T ^(1//2)`