Calculating Age with Radioactive Decay
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Calculating Age with Radioactive Decay

[From: ] [author: ] [Date: 12-08-31] [Hit: ]
Assume the meteorite itself is a closed system.I understand the concept of half-life (after 1.3 billion years the radioactivity of K will be half the original, and in 2.6 a quarter, etc) but I do not understand the relationship between K and Ar,......
The Question: A meteorite is found in the North Carolina with 4 milligrams of 40K and 12 milligrams of 40Ar (and other daughter isotopes). When (in billions of years) was this meteorite formed? The half-life of 40K is 1.3 billion years. Assume the meteorite itself is a closed system.

I understand the concept of "half-life" (after 1.3 billion years the radioactivity of K will be half the original, and in 2.6 a quarter, etc) but I do not understand the relationship between K and Ar, or what exactly to do with the 4mg /12 mg.
Thanks

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40K is the parent. Parent + daughter = 12 + 4 = 16 mg. There is 1/4 (4/16) parent and 3/4 (12/16) daughter. This corresponds to two half-lives elapsed.
The age is 2*(1.3 billion) = 2.6 billion years.

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the notion is "daughter element"
we cannot tell the age if we simply find some radioactive element, because we do not know how much was there to start.
BUT, if we know the "daughter" could only come from the parent, and we know the rates of formation and decay, there are methods of working backwards to the assumed start

in the case of rocks, when they first became solid and the material was fixed in place is the "beginning"
you need the half life of each from careful lab experiment and observation

in half life decay you must assume pure chance and very large numbers. there is no way to predict when an individual atom will decay

in Atomic piles the presence of Neutrons can induce decay in other U atoms and change the rate from billions of years to micro seconds, ( Japan will tell you that)
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