Question

On any planet, the presence of atmosphere implies [ ${V_{rms}}$ is root mean square velocity of molecules and ${V_e}$ is escape velocity ]

(A) ${V_{rms}} \ll {V_e}$
(B) ${V_{rms}} > {V_e}$
(C) ${V_{rms}} = {V_e}$
(D) ${V_{rms}} = 0$

Answer 1

Hint: Here in order to get the answer for this question you need to know the conditions for the presence of atmosphere in any planet. What are the conditions required for it, what is root mean square velocity and what is escape velocity then only you can tell about its relation that is required for the presence of atmosphere.


Complete answer:
For the presence of the atmosphere in any planet;
There should be the required molecules present in the planet that ultimately form the atmosphere in that planet.

For atmosphere to be present,
The root mean square velocity needs to be much smaller than the escape velocity, So that all the required molecules will be present that form the atmosphere and they do not escape.
If ${V_{rms}} < < {V_e}$ then only the atmosphere will be present.
Where, ${V_{rms}}$ is root mean square velocity
${V_e}$ is escape velocity

If ${V_{rms}} \geqslant {V_e}$ , root mean velocity is equal to or greater than escape velocity then all the required molecules or gases will disappear from the planet and hence no atmosphere will be formed.
This is the reason why there is no atmosphere on the moon because their escape velocity is less than root mean square velocity.

Hence the correct answer is Option(A).




Note: Know the basics of root mean velocity and escape velocity, what type of relation they have in between them and how they are related to the formation of the atmosphere. If the gases escape the gravitational field of the planet then there will be no atmosphere formed on the planet.