The ratio of escape velocity of Helium, Argon and Xenon is 31.5 %, 10.0 % and 5.5 % respectively.
Calculation:-
taking T = 2000 K and R = 8.315 J mol-1 K-1
Molar mass for Helium = 4.0026 x 10?3 kg mol-1
Molar mass for Argon = 39.948 x 10?3 kg mol-1
Molar mass for Xenon = 131.29 x 10?3 kg mol-1
We get the rms speed for the given gases as followed
Helium = 3.53 km s-1
Argon = 1.12 km s-1
Xenon = 0.62 km s-1
The ratio of the escape velocity to the root-mean-square speed of the given gases
The ratio of helium = 31.5 %
The ratio of argon = 10.0 %
The ratio of xenon = 5.5 %
Yes, the fraction (or ratio) of the speed exceeding the escape velocity (31.5%) is larger in helium, which makes low abundancy of the helium in the atmosphere.
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