Thursday, 19 April 2012

atmosphere - Why argon instead of another noble gas?

Doing a bit of reading up on this, I might have an answer, though credit where credit is due, the answer isn't really mine:



https://www.reddit.com/r/askscience/comments/3wsy99/why_is_neon_so_rare_on_earth/



When the planets coalesced, it's likely that there was very little ices/gas around the inner planets when they formed and the Earth's atmosphere and water (CH4, NH3, CO2 and H20 being the 4 most common outside the frost line ices). These likely came from asteroids and meteors that formed outside the frost line and later crashed onto earth.



Neon is the 5th most common element in the milky-way but because all noble gases have very low freezing points, it's likely not be very common even on comets or meteors for the same reason that water or CO2 aren't common inside the frost line, Neon, and other noble gases likely stay free and don't collect on comets or meteors in high amounts. (I looked, but couldn't find an article to verify that).



But if comets have low noble gas content, then we have to look for an alternate source. With that in mind, and going back to the first link, Argon is produced by radioactive decay of Potassium 40 and that would explain it's relative abundance compared to the more common noble gas, Neon. Helium (Alpha particles) is also produced inside the earth and Radon is is too in small amounts but Radon also decays - that's not related to your question though.



If Argon on planets comes primarily from Potassium 40, you should expect the amount of Argon to have a roughly similar ratio to the amount of potassium on a planet and not be relative to the percentage of atmosphere. A 2nd factor, how much gets blown off the planet over long periods of time is a factor too. Venus in general should be able to retain much of it's Argon based on atomic weight (40) similar to CO2 (44), but if it loses even a tiny percentage of it's Argon over time, that would be a factor too.



Now, to see if this is possible, I should run some numbers, but I warn you, my math can be a little rusty.



Potassium is the 7th most common element in the Earth's lithosphere at about 0.26% and about 0.0117% of that Potassium is Potassium 40. Using a very rough estimate of 2.3 x 10^19th tonnes for the Earth's crust, 2.3*10^19*2.5*10^-3*1.17*10-4 = about 6.7*10^12 or 6.7 trillion tons of Potassium 40 currently in the Earth's crust. (There's probably a fair bit more in the mantle, so these numbers are rough)



With a half life of about 1.248 billion years, that's sufficient time for over 3 half lives if we start after the late heavy bombardment, which suggests a bit over 7/8ths of the original Potassium 40 in the Earth's crust has decayed into Argon 40, so there should be, given the age of the Earth and abundance of Potassium 40, a bit over 7 times 6.7 trillion tons or, lets ballpark and say a bit over 50 trillion tons of Argon that formed on earth by Potassium decay. (I'm ignoring any that might have been produced prior to the late heavy bombardment, cause I assume that could have blown some of the atmosphere off the earth or heated the atmosphere enough for the sun to blow some of it off). Also, doing a bit of research, only 11% of the Potassium 40 decays in to Argon 40, 89% undergoes beta decay into Calcium 40, so for this to work, there would need to be a fair bit more Potassium in the earth than I estimated, but that's still likely the case.



The mass of the atmosphere is about 5,140 trillion tons, and 1.288% of that (By mass, not volume) = about 66 trillion tons, so the Argon we should expect from Potassium 40 decay and the amount of Argon in the atmosphere are pretty close. Some Argon gas might have escaped and some should still be trapped inside the earth but the numbers are close enough to work and I think that's very likely the answer. It also suggests that the Earth has lost relatively little Argon to space, which also fits with the Atmospheric Escape article.



A 2nd way to look at this is that Argon 40 makes up 99.6% of the Argon in the atmosphere and Stellar Nucleosis likely wouldn't account for a ratio anywhere close to that (not a typical stellar link but Wikipedia says Argon 36 is the most common isotope). The decay of Potassium 40 does explain the 99.6% Argon40 ratio.



If we apply a similar estimate to Venus, with Venus atmosphere about 94 times the mass of Earth's, and we assume a similar amount of Argon-40 being produced in Venus' crust we could roughly expect 1.28%/60 or about 0.02% Argon by mass in Venus's atmosphere or perhaps, if the Earth lost a pretty high share of it's lighter crust elements after the giant impact, we might expect a bit more than that on Venus, perhaps 0.03% or 0.04% as a rough estimate. Using your number of 0.007%, that's lower than I calculate it should be, but Venus could have lost a higher share of it's Argon than Earth and it also might be slower to release trapped gas inside it's crust than Earth because it doesn't have plate tectonics, so the number for Venus looks "about right" too. It's the Potassium 40 in the crust. I'm convinced.



Interesting question. I learned something researching it.

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