Radio-dating and the age of the earth

I understand there are a few radio-dating methods to determine the age of the earth, uranium-lead to name one (maybe not the best though). The ratio Pb206 + Pb207 to U allows you to find when the uranium came into existence. What I don't understand is how this relates to the age of the earth. Can't the uranium have been rambling for 500 million years in space before lumping together with other elements to form the earth? Which would make the age of the earth in this case 4 billion years instead of 4.55 billion.

Or is it the same as with C14 dating: the C14 is formed in the higher atmosphere through interaction of cosmic rays with nitrogen atoms. This stops when the carbon enters living material, so we know then the decay starts. Is the radioactive uranium created by cosmic rays until it hits earth? But the early earth didn't have an atmosphere which would stop the cosmic rays, did it?

So I'm a bit confused. How do we know the uranium formed at the same time as the earth?

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Yes, all Uranium in the Solar System was formed long before the birth of Earth. But, we don't consider any Uranium rock to calculate age of Earth. We use Zircon minerals (there're other standard minerals, too).

At the time of formation of Earth, Zircon minerals were formed. Zircon mineral formation includes Uranium atoms into crystalline structure, but rejects lead. Meaning, a rock of Zircon started its life with zero lead. But, due to the radioactive decay of Uranium atoms, - today - we can find some lead in a Zircon rock. As Half Life of Uranium is known, we can use Uranium-Lead ratio to calculate the age of Earth.

Suppose a Zircon rock included 1Kg Uranium at the time of formation. After one half life, it'd have 0.5Kg Uranium and 0.5Kg Lead. Using this data, you can calculate the age of the rock. But, you may ask: What if the rock is broken into pieces and we find only a part getting wrong data?
That's a valid question, but the thing is: Zircon is one most durable rocks on Earth. It's immune to any chemical reaction. And, Uranium inclusion happens on crystal lattice level. Meaning, we just need crystal grains, not the entire rock.

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+1 Very thorough answer - I really enjoyed reading it. – WetSavannaAnimal aka Rod Vance Apr 24 '14 at 23:39

I think this article should explain: Zircon Chronology: The Oldest Material on Earth

Zircon is an extremely durable mineral, once zircon crystals have formed, they can last billions of years. It is a well understood chemical process that produces zircons, they crystallize today from crustal magmas. Zircons are common on earth, it is reasonable the that the oldest zircons we find in terrestrial rocks are a lower bound on the age of earth's crust.

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The Wikipedia article contains a good explanation of this. The technique is usually applied to crystals of Zircon that initially contain little or no lead. Any lead found in the crystal must have come from uranium decay.

Uranium is created in supernovae. The Earth's surface doesn't contain significant amounts of any material that could be transmuted to uranium by bombardment with cosmic rays (i.e. high energy protons).

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So as long as whatever process formed the Earth also differentiated the parent and daughter isotopes that were present in the solar nebula (not an unreasonable assumption), then there is no reason to expect that enough daughter isotopes in a radioactive sample would be older than the formation event to affect the measurement. Similarly for volcanic rocks, which lose daughter isotopes to the air during an eruption. – Michael Brown Mar 5 '13 at 8:16
I'm aware of zircon. But if it doesn't contain any lead it must have formed very recently, maximum tens of millions of years ago. And if the uranium is older there must be lead somewhere, not incorporated in the zircon. So you have an amount of uranium, of which you don't know how many percent of the original it is. And without this ratio there's no dating. – stevenvh Mar 5 '13 at 10:22
Zircon crystals won't incorporate lead, so at the moment of formation it contains some concentration of uranium and no lead. One half life later there are equal numbers of uranium and lead atoms. Two half lives later the lead:uranium ratio is 3:1, and so on. Hence the lead:uranium ratio gives the time since the zircon crystal formed. The ratios for $^{238}$U:$^{206}$Pb and $^{235}$U:$^{207}$Pb can be measured separately to reduce experimental error. This assumes no lead is lost from the zircon crystal. – John Rennie Mar 5 '13 at 10:35