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

Asked in JEE Main Online 2014 · Escape speed and Brownian motion

• (1) 0
• (2) (273k_B)/(2Mg)
• (3) (546k_B)/(3Mg)
• (4) (819k_B)/(2Mg)

Step-by-step solution

Why the other options are wrong

• (1) The molecule does rise; it has a real kinetic energy at 0°C.
• (2) Comes from using 1/2 k_BT, the energy of a single degree of freedom, instead of the full 3/2 k_BT.
• (3) Comes from using k_BT (two degrees of freedom) and then misplacing the fraction.

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