Question 17: Escape velocity from the Earth refers to the minimum speed an object must have to leave the Earth and never return. (a) The escape velocity from the Moon is about one-fifth what it is for the Earth, due to the Moon’s smaller mass. Explain why the Moon has practically no atmosphere. (b) If hydrogen was once in the Earth’s atmosphere, why would it have probably escaped?

The average translational kinetic energy of the molecules in random motion in an ideal gas is directly proportional to the absolute temperature of the gas.

The average translational kinetic energy is

\(\overline {KE} = \frac{1}{2}m\overline {{v^2}} = \frac{3}{2}kT\). ... (i)

Here, k is the Boltzmann constant, m is the mass of each molecule, and \(\overline {{v^2}} \) is the average of the square of the velocity of the molecules.

The escape velocity of a molecule from the Moon is one-fifth of that from the Earth. Since escape velocity refers to the minimum speed required by an object to leave the planet, therefore the value of minimum speed required by the molecules constituting the atmosphere to leave the planet is very less on the Moon as compared to that on the Earth.

The molecules comprising the atmosphere on the Moon would easily escape even with a lower speed, and with time, there would be no molecules left on the Moon. Therefore, practically, there is no atmosphere on the Moon.

At a given temperature, molecules constituting the atmosphere have a fixed average kinetic energy. From expression (i), for a given kinetic energy, the mass of a molecule is inversely proportional to its speed.

Since the mass of the hydrogen molecule is the least, it has the highest speed. So, hydrogen molecules can more easily escape the Earth than the molecules of other gases in the atmosphere.