A nitrogen molecule at the surface of earth happens to have 'rms' speed for that gas at `0^(@)C`. If it were to go straight up without colliding with other molecules, how high would it rise? (Mass of nitrogen molecule, `m=4.65xx10^(-26) kg,R=8.3J//mol//K`)

Explanation

The molecule goes to a height h till its entire KE is converted into P.E
`threreforemgh=(1)/(2)m(v_(rms))^(2), h=((v_(rms))^(2))/(2g)=(3RT)/(M2g)`
`=(3xx8.31xx273)/(28xx10^(-3)xx2xx9.8)=12.4km`