When the solar system formed from the nebula, only the massive gravitation enabled the gas giants - Jupiter, Saturn, Neptune etc - to retain the lighter inert gases such as helium. The ones heavier than argon are very rare as mole fractions and only a vanishingly small fraction have escape velocities of > 11.2 km/sec at about 600 K, the temperature in the Earth's thermosphere, where the mean free path is long enough that molecules can follow ballistic trajectories into space. Argon-40 alone has a local source, from the radioactive decay of potassium-40 that has been operative since the formation of the nebula and which continues in Earth's interior. The escape velocity of O-16 atoms from Earth is higher than that of argon-40, and yet Earth has retained its oxygen: only about 10**-84 O atoms have velocities at 600 K large enough to escape Earth's gravitational field. A fuller account can be found in "The Elements: their origin, abundance and distribution", P A Cox, OUP, 1997.

Dear Prof. Kenneth,

First of all my sincere thanks for your answer.

Now, I understand that most of the atmospheric Argon are produce by the following reaction.

19K40+e⟶18Ar40+γ+νe

with half-life of 1.25×109 years.

It means, the radiogenic argon are very very stable in nature.  In such case the above reaction also keep on happening in the earth crust, right? Is it mean the Argon concentration will increase in future, if it will not means why?

thanking you,

With warm regards,

Sivakandan M

NARL

India.

When the solar system formed from the nebula, only the massive gravitation enabled the gas giants - Jupiter, Saturn, Neptune etc - to retain the lighter inert gases such as helium. The ones heavier than argon are very rare as mole fractions and only a vanishingly small fraction have escape velocities of > 11.2 km/sec at about 600 K, the temperature in the Earth's thermosphere, where the mean free path is long enough that molecules can follow ballistic trajectories into space. Argon-40 alone has a local source, from the radioactive decay of potassium-40 that has been operative since the formation of the nebula and which continues in Earth's interior. The escape velocity of O-16 atoms from Earth is higher than that of argon-40, and yet Earth has retained its oxygen: only about 10**-84 O atoms have velocities at 600 K large enough to escape Earth's gravitational field. A fuller account can be found in "The Elements: their origin, abundance and distribution", P A Cox, OUP, 1997.

I may have created the impression above that O and Ar have different escape velocities. They don't of course, escape velocity is mass independent. The fraction of molecules having velocity >11.2 km/sec is greater for lighter molecules, so Ar-40 will have a fraction [40/16]**-1/2 less than O-16, since assuming Maxwell-Boltzmann speed distributions has velocity inversely proportional to the square root of mass. As far as the cold trap goes, it is a very uncertain calculation away from the present, because the cold trap T depends on the lapse rate which in turn depends on atmospheric composition. Estimates of Earth's surface temperature range from 80C to freezing (the latter during any 'snowball earth' episodes), and the carbon dioxide partial pressure from 10**-3 bar to 10 bar. Since water vapour is the principal 'greenhouse' gas, it's nonlinear with very large error possibilities. Once photodissociation of water vapour is allowed in the thermosphere, the calculation becomes more quantum mechanical, because the velocity of the photofragments will be boosted by the O-H bond energy.