The root mean square velocity of a gas molecule of mass m at a given temperature 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 , `v^(-2)=(3RT)/(M)rArrv_("rms")=sqrt((3RT)/(M))`
The root mean square speed of the molecules of a gas is directly proprotinal to the square root of the absolute temperature of the gas and inversely proprotional to the square root of the mass of molecules of the gas.
`So, " " v_("rms")propsqrt(T)and V_("rms")prop(1)/(sqrt(m))`
`or, " " v_("rms")=m^(-1//2)xxT^(1//2)`