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A certain moon rock was found to contain equal numbers of potassium and argon atoms. Assume that all the argon is the result of radioactive decay of potassium (half life $1.28 \times 10^9$) and that one of every 9 potassium atom disintegrations yields an argon atom. What is the age of the rock measured from the time it contained only potassium.

please suggest

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    This question doesn't seem to make sense; what happens to the other 8 out of every 9 potassium decays? Unless we treat them as disappearing completely, or decaying into another potassium isotope, there will be a third substance in the rock.2011-08-17
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    @Zev: I don't think that affects the relative quantity of potassium and argon atoms, does it? The question only states that the rock contains equal numbers of potassium and argon atoms, not that, say, 50% of all the atoms are argon.2011-08-17
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    Aha, you're correct, Rahul. I'm doing terribly today it seems...2011-08-17
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    Ordinary potassium contains a very rare radioactive isotope. The other isotopes are not radioactive. It is utterly impossible for the ordinary mix of potassium isotopes to end up half potassium and half argon. One has to assume that by potassium the author means the radioactive version only.2011-08-17

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