|MadSci Network: Physics|
You ask a very good question. The answer comes in a few parts, but they all share a common theme: nature has processes that like to seperate materials based on various physical and chemical properties. You've seen this in your every day life. For example, a well-mixed bottle of salad dressing will be stratified into different components by the next day if you don't touch it.
The first time we see nature being picky about materials is in the actual building of rocky, Earth-like planets. You would think, at first guess, that everything in the universe would be made almost entirely of hydrogen and helium, since those two elements make up most of the universe. Stars, for instance, are made almost entirely of these two components. But planets, especially the inner four in our solar system, have very little of these two elements and are made up of much rarer stuff. How did that happen? The answer is heat. Our planet formed pretty much where it is today relative to the center of the solar system. Then, as now, it was hotter around here than in distant parts of our system. (Although I should note that back then it was not because of the Sun's warming glow.) At these temperatures, hydrogen and helium are gases and don't like to stick around small objects like the inner planets. The hydrogen compounds like water, ammonia, and methane - all very common in the outer solar system in their icey forms - are also gases, and so also remain aloof of the planet formation process. So Mercury, Venus, Earth, and Mars could only be built out of heavier stuff that could exist in a solid form at the higher temperatures, like rocks and metals. (Including uranium, although it was still a very minor player.)
So now we have a planet that is made of rock and metals. But everything is all mixed up, and the uranium still isn't very purified at all. Happily, there is more.
Early in Earth's life it was very hot and very molten. Stuff was able to flow around freely. And, as your exprience with salad dressing suggests, that leads to the dense materials sinking to the bottom of the bottle. Or, in the case of Earth, into what is now the core. The dense stuff in this case was the iron and some other elements that like hanging out with iron. Since iron makes up a lot of the Earth's mass, this left the stuff near the top more purified than it was before. So now there's more uranium in each handful of (watch out, it's still molten!) Earth.
Here's the last part. As the liquid rock cooled off, minerals started to crystalize. Each mineral crystalizes at a different point in the cooling process, so there is some order. The minerals tend to be either more or less dense than the molten rock that is left, so they float or sink out of the liquid. At some point, pitchblende (the ore in which you'll find uranium) crystalized and left the liquid. This results in chunks of pitchblende which aren't really mixed with all the other minerals which make up Earth's crust.
This also works with other ores, like bauxite (aluminum), taconite (iron), hematite (also iron), and so forth. In fact, it works with any mineral you like. The last process is still occuring, since the interior of the Earth is still molten and since plate tectonics cause nice, solid rocks to be remelted then recooled all the time.
If you want to learn more about the planet formation processes, I recommend The Cosmic Perspective, a very good astronomy textbook by Bennett, Donahue, Schneider and Voit. (If you can't find that one, take a peek in whatever astronomy textbooks you can find. You'll probably still find a good explaination.) You can also visit The Nine Planets Website where they have an overview planet formation. If you're interested in the last process I mentioned, where materials crystalize out of the molten rock, I suggest a good geology textbook. The one on my shelf is Physical Geology, by Monoroe and Wicander, but I'm sure others also discuss the process. (If you experience difficulties finding the right section in the textbook, try looking up "Bowen's Reaction Series" in the index.)
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