A gas molecule of mass M at the surface of the Earth has kinetic energy equivalent at $\;0^{0}C\;$.If it were to go up straight without colliding with any other molecules , how height it would rise ? Assume that the height attained is much less than radius of the earth .($\;k_{B}\;$ is Boltzmann constant)

Question

$(a)\;0\qquad(b)\;\large\frac{273k_{B}}{2\;Mg}\qquad(c)\;\large\frac{546k_{B}}{3\;Mg}\qquad(d)\;\large\frac{819k_{B}}{2\;Mg}$