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

• A

  $\frac{273k_{\mathrm{B}}}{2Mg}$
• Correct answer
  B

  $\frac{819k_{\mathrm{B}}}{2Mg}$
• C

  $0$
• D

  $\frac{546k_{\mathrm{B}}}{3Mg}$

Hence, the correct answer is option: 'B'.