From kinetic theory of gases, show that Moon cannot have atmosphere (Assume `k=1.38xx10^(-23)JK^(-1),T0^@C=273K)`.

Explanation

We know that `1/2mV^2_(rms)=3/2kT`
`:.V_(rms) = sqrt((3kT)/m)`
mass = `3.33xx10^(-27)kg`
Temperature = 0+273=273K
Boltzmann constant `k = 1.38xx10^(-23)J//K`
`:.V_(rms)=sqrt((3xx1.38xx10^(-23)xx273)/(3.33xx10^(-27)))`
`= sqrt((3xx1.38xx273)/(3.33)xx10^4)`
`=18.422xx10^2`
`V_(rms) =1.842xx10^3ms^(-1)`
The value of `v_e` is less than the velocity of gass present on mon . Hence moon cannot have an atmosphere.