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There's an awful lot of argon in the atmosphere: about 0.93% of the atmosphere is argon[1], making it the third-most abundant gas after N2 and O2. As I understand it, most of it is produced by the following decay path:

$$ \ce{^{40}_{19}K + ^{0}_{-1}e- -> ^{40}_{18}Ar + \gamma{} + \nu_{e}} %edit $$

How does all this radiogenic argon make it into the atmosphere, though? Most of the decaying potassium-40 must surely be at some depth beneath the surface, thus trapping the argon-40 in the interior of the Earth, right?

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As the previous responder noted, the continental crust forms a large reservoir of potassium. Much of this is in the form of feldspar. My answer primarily addresses this continental crust source. To get to the atmosphere, argon produced from the decay of 40K in the crystal lattice first must either diffuse out of the structure or be released during mineral alteration. Argon will be released through weathering of potassium feldspar to clay minerals. This can occur in the near surface environment or at greater depth from hydrothermal alteration or by deep circulating groundwater. Depending on your perspective, this released argon is no longer 'trapped' although there will be a concentration gradient towards the atmosphere (for example there is build-up of 40Ar in the Great Artesian Basin of central Australia). It does not necessarily take volcanic activity to release argon to the atmosphere. To quote Graham, DW (2002) Noble Gas Isotope Geochemistry of MORBs and OIBs in Noble Gases in Geochemistry and Cosmochemistry Reviews in Mineralogy & Geochemistry V. 47:

"Transport of [40Ar] to the atmosphere involves volcanic degassing, hydrothermal circulation through the crust, and erosion of continental crust..."

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Most of this 40Ar makes its way to the atmosphere in two primary ways. Firstly, since most of the K is concentrated in the continental crust, volcanic eruptions on the continents over geological time have concentrated Ar in the atmosphere. Since it is too heavy and inert to decrease in any appreciable method it has a long residence time. Secondly, volcanism at mid-oceanic ridges releases Ar into the ocean and then into the atmosphere. The current combined rate of these volcanic events is ~ 2.2×109 grams/year.

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