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The number of <sup>238</sup> U atoms in ...

The number of 238 U atoms in an ancient rock equals the number of 206 Pb atoms. The half-life of decay of 238 U is 4.5x109 years. Estimate the age of the rock assuming that all the 206 Pb atoms are formed from the decay of 238U.

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Since the number of `.^(206)Pb` atoms equal the number of `.^(238)U` atoms, half of the original `.^(238)U` atoms have decayed. It takes one half-life to decay half of the active nuclei. Thus, the sample is `4.5 xx 10^(9)` years old.
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