Re: Shrinking Earth

In article <iPBkf.11054$ea6.6251@xxxxxxxxxxxxxxxxxxxxxxxxxx>, Chriso
wrote:
> Radioactive elements in the earths core could fission
> and split into 2 elements, thus occupying twice the space.
>
> Over geological time the mass of the earth would remain the
> same but the volume it occupied would increase markedly.
>
Hmmm, interesting (about the only interesting thing to come out
of Don's obsession).
A for-instance :
Uranium -> I + Rb + He
Atomic number 92 53 37 2
Ionic radius (Å) 0.52 2.2 1.52 Gas

So yes, there's at least the potential for appreciable increases
in volume on fission. You'd have to do a much more thorough-going
analysis to account for the different proportions of the different
fission reactions at different probabilities, but there's one datum
which summarises the result : after a number of years inside nuclear
reactors, the fuel elements often undergo physical distortion. Some of
that is going to be accumulation of helium, some of it is going to be
reaction of the fuel element's cladding with the heat exchange medium.
And some of it a volumetric increase due to fission. That's an issue in
why there's a need for fuel re-processing (apart from the need to
divert plutonium from civil power generation to bomb-making).
Now for the important question though. Volumetrically, what
proportion of the earth's interior is composed of radioactive atoms?
Element Cosmic abundance ( atoms per 10^12 atoms H2)
U < 4
I 44
Rb 410
He 80,000,000,000
O 690,000,000 and a few others ...
Fe 25,000,000
Mg 32,000,000
Si 40,000,000
Now, to a fair working approximation, the Earth consists of
general cosmic abundance of elements, minus the gasses. (I know it's a
bit crude, but it'll get us to within an order of magnitude - a factor
of 10 - either way.) The bulk composition is not going to be far off Fe
MgSiO4, and the uranium would be 12 parts in 97 million of that (add up
the appropriate amounts of Fe Mg and Si and vent all the oxygen that's
not tied up to those ions; quick and dirty estimate). So ... if all the
uranium in the Earth fissioned tomorrow, with an average change in
ionic radius of a factor of about 4 (as above), you'd get a volumetric
change (for the U) of about x 64 (plus some gas, which would vent in a
geological eye blink). That's a volumetric increase of 64 times the
original volume of the uranium. But for the whole earth ... 12 parts in
97 million would go to 768 parts in 97 million, a change of 756 parts
in 97 million, or 1 part in 128,000.

It's a real effect. But it's not a very big one.
--
Aidan Karley FGS
Aberdeen, Scotland,
Location: 57°10'11" N, 02°08'43" W (sub-tropical Aberdeen), 0.021233

.

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