On any planet,the presence of an atmosphere i | vedclass

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Question

(A) The presence of an atmosphere on any planet implies that $C_{rms} < V_e$.

Vedclass · Accepted Answer

$C_{rms} << V_e$

Vedclass · Answer

(A) The presence of an atmosphere on any planet implies that $C_{rms} If the root mean square velocity $(C_{rms})$ of the gas molecules were equal to or greater than the escape velocity $(V_e)$,the molecules would possess enough kinetic energy to overcome the planet's gravitational pull.Consequently,the gas molecules would escape into space,and the planet would not be able to retain an atmosphere.Therefore,for an atmosphere to exist,the average speed of the molecules must be significantly lower than the escape velocity.

On any planet,the presence of an atmosphere implies ($C_{rms}$ = root mean square velocity of molecules and $V_e$ = escape velocity):

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