How much more heat did radioactive decay generate 2 and 4 billion years ago?

[udtsith]

I read a recent article (pc magazine) that said the Earth is currently generating 44 terawatts of heat with 23 terawatts comign from radioactive decay (8 from uranium, 8 from thorium, and 4 from potassium). Given this, and that the Earth is 4.5 billion years old...how many more terawatts were coming from radioactive decay at 2 billion and 4 billion years ago?
What sort of affect would this have had on life and the continents moving?

 

[Nik_2213]

Well, primordial plate tectonics and any extant 'ring of fire' were probably much livelier. The extra heat may have helped create 'diamond pipes', as they all seem ancient, and we don't seem to see such eruptions any more. Also, there was enough uranium about for at least one (1) area to have groundwater moderate a natural nuclear reactor...
http://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor
http://en.wikipedia.org/wiki/Diamond

 

[IsometricPion]

Assuming the longest-lived (radioactive) isotopes of those elements are producing the heat, the decay constants are: K40-1.248E9 yrs., U238-4.537E9 yrs., Th232-1.40E10 (ref. http://www.nndc.bnl.gov/chart/" ). Given the amount of a radioactive element present now,N₀, the amount a given time, t, ago would be N(t)=N₀e^t*ln(2)/D, where D is one of the half-life values given above. Assuming the amount of heat produced is proportional to the rate of decay, H(t)=H₀e^t*ln(2)/D, where H₀ is the amount of heat being produced by the element today. Adding up the values for each of the elements I get: H_now= 20 TW H_{2 Gya}≈ 32 TW H_{4 Gya}≈ 61 TW. I cannot speak definitively on your last question, but since the largest value is only about 3 times larger than the current one I doubt there would be a large qualitative difference (maybe volcanos would have been somewhat more common and plate tectonics somewhat faster). Life is not likely to have been greatly influenced by this extra heat (at least not directly, though the geological effects might have had some influence) since the Sun usually provides much more heat. Of course it is possible that other sources of radioactivity were also significant long enough ago (so my estimate above is more of a lower bound on the amount of heat due to radioactivity at those points in the past).

 

[MrGamma]

So if 23 TeraWatts is coming from radioactive decay. Then should that mean that in relative proportion to the size of the Earth, the Moon will be generating the same if the theory of a large early impact is its origin?

(maybe volcanos would have been somewhat more common and plate tectonics somewhat faster)

I am not a geologist or a volcanist, so I could have this wrong, but there are some ancient volcanoes, which are said to have erupted somewhat unique material, probably due to the high temperatures, not entirely sure...

"No modern komatiite lavas are known, as the Earth's mantle has cooled too much to produce highly magnesian magmas."

Ultra Mafic - http://en.wikipedia.org/wiki/Lava#Ultramafic_lava

 

[DoggerDan]

So if 23 TeraWatts is coming from radioactive decay. Then should that mean that in relative proportion to the size of the Earth, the Moon will be generating the same if the theory of a large early impact is its origin?

The Earth is not homogeneous. Therefore, if the Moon is a chip off the old block, who's to say it's a homogeneous chip? More than likely it took a large chunk of mantle.