find the radius such that oxygen is detained in the atmosphere [closed]

Find the minimum radius of planet with mean density $\rho$ and temperature $T$ which can detain Oxygen in its atmosphere and $G$ = Universal Gravitational Constant and $M$ is molecular mass of Oxygen gas.

I tried to do it with the kinetic energy of oxygen molecule as $K.E$=$\frac{5mRT}{2M}$ and then equating it with the potential as $\frac{GMm}{R_{planet}}$ but I am getting the wrong answer. Here I assumed that mass of gas is $m$. $$\frac{5mRT}{2M}=\frac{G\rho \frac{4\pi}{3}R^3m}{R_{planet}}$$ Whats wrong with this method?

• I used the mean density While writing the mass of planet as $rho$=$\frac{Mass of planet}{Volume of planet}$ and why would need to consider effect of gravity on single particle because even if we consider the mass m it would get cancelled from both sides.?? – Piyush Raut Jan 17 '17 at 13:49
• try KE$=3kT/2$ for one molecule of mass M – JMLCarter Jan 17 '17 at 17:38