Posted: Apr 01, 2010 7:13 am
Beelzebub wrote:OK, here's a question - why should the Earth contain any radionuclides at all?
Do we know what proportions of isotope to parent element are created in a supernova explosion (assuming, for now, that that is where they originate from) ?
If a supernova occurred, say, 4 billion years before the Earth formed, then wouldn't all but the longest-lived isotopes have decayed by then? Is it legitimate to consider the supernova as being contemporary to the formation of the Earth?
Just asking, as I'm sure others have thought of similar questions...
In the case of elements produced by a supernova detonation, what happens is that they are formed in stages by neutron absorption followed by beta decay along the neutron drip line. The immediate environment surrounding a supernova detonation is nicely rich in neutrons, facilitating the building of the requisite elements. Indeed, the relevant physical theories governing this have been given a nice evidential boost courtesy of long term observation of SN1987A, which has yielded the spectra of new elements appearing over time.
The next matter to consider is the vast mass of material involved. Stars that produce supernova detonations at the end stages of their lives are massive - the minimum mass is of the order of 8 solar masses, and quite a few stars that evolve to the supernova stage are a good deal more massive than that. So there's quite a lot of material shed into the surroundings when a supernova detonates. If that material then comes into contact with a relatively close gas cloud of light elements such as hydrogen and helium, it can form the basis for an accretion disc should the interaction trigger star formation within the light gas cloud. A compression wave travelling through the gas cloud as a result of the interaction would introduce density inhomogeneities in the gas cloud, and gravity would then do the rest.
Turning to Kaye & Laby, we have a nice table featuring the abundances of the elements. The column for the Solar System is represented in rather odd units: the figure is the number of atoms present for each 106 atoms of silicon (which is a nice, easily measured, relatively abundant element). So, for every 106 atoms of Si in the Solar System, there are 2.8 × 1010 atoms of hydrogen. However, there are a lot more than 106 atoms in the Solar System in total. For example, the mass of the Sun is 1.9891 × 1030 Kg, of which 75% is hydrogen. A mole of hydrogen atoms (note: NOT hydrogen molecules!) has a mass of 1 gram, therefore 1 kilogram of hydrogen atoms equals 1,000 moles, and each mole comprises 6.023 × 1023 atoms, so this gives us that the Sun alone contains around 8.985 × 1056 hydrogen atoms. Since the Sun comprises 99.86% of the entire mass of the Solar System, that means that the total abundance of hydrogen in the Solar System is around 8.997 × 1056 atoms. Divide this by 2.8 × 1010 to obtain our multiplying factor, and use this to multiply the entries in the table to obtain the actual total number of atoms in the Solar System, and we have, for uranium, 5.785 × 1044 atoms throughout the Solar System, the majority of which are concentrated in rocky bodies such as the Earth. Apparently, the spectrum of the Sun contains no measurable lines for uranium, though oddly enough it does contain measurable lines for thorium, and the abundance of thorium in the Sun is slightly higher than that for the Solar System as a whole - a little puzzle that should keep some researchers happy for a while.
Now, given that we can plot the distribution of stars of various masses, and indeed, astronomers have already done this, it transpires that something of the order of 0.1% of all stars in the current population are of 8 solar masses or greater, and therefore destined to end in supernova detonations, but of course that's the stars extant after 13.6 billion years of the life of the universe - things become more complicated when we consider the first population of stars to form early in the life of the universe, but that's a separate topic properly deserving its own thread. Basically, something like 0.1% of all stars have masses greater than 8 solar masses (if you want the precise figure, find a tame astrophysicist!) and these stars have lifetimes of only 10 million years or so. For example, Zeta Orionis is a hot blue supergiant whose mass is around 28 solar masses, and Zeta Puppis is an extreme example of this sort of star, with a whopping 64 solar masses to its credit. Nearing the end of its life is Antares, a red supergiant with a mass of 15.5 solar masses, and since Antares is only 600 light years from Earth, when it blows, it'll light up the night sky in spectacular fashion. It will also send a fair amount of matter our way, and that matter will form a nebula of truly stupendous proportions visually as it grows, becoming the dominant feature of the night sky for millennia. But I digress. If you want to find out more about this, useful links include this one and this one. But if you want the current record holder, that will be Eta Carinae, a star that is estimated to possess a mass of as much as 150 solar masses, and when that goes supernova, we'll certainly know about it, even though it's 8,000 light years from Earth.
Basically, stars of the size of Eta Carinae and Zeta Puppis will dump a LOT of heavy element debris into the surroundings. Untold trillions of tons of the stuff. Even a more modest supernova will dump something like 5 × 1030 Kg of material into space. That's a lot of atoms. Even if only one kilogram in 1010 Kg of that material ends up as a uranium atom, you're still going to end up with 5 × 1020 Kg of uranium. After 4.5 billion years, you'll still be left with around 2.5 × 1019 Kg. So you shouldn't be surprised that there's still useful amounts of uranium available for us to pop into nuclear reactors.