A particular rock is thought to be 260 million years old. If it contains 3.10 mg

Question

A particular rock is thought to be 260 million years old. If it contains 3.10 mg of U-238, how much Pb-206 should it contain ? (use half-life = 4.47 times 10^9 y, assume no initial Pb, and that Pb-206 is considered the direct daughter product of U-238 decay - acceptable given that U-238 is by far the longest lived isotope in the decay chain) Note: The Molar Mass values given in tables for chemical elements are for natural mix isotopic ratios, (i.e. the relative percentages of each isotope normally present in natural samples). The Molar Mass (in g/mol) for a pure isotope is equal to its atomic mass (in amu). (Answer in mg, correct to 3 significant figures)

Explanation / Answer

let x be the required amount:
(x/206) / (3.1/238) = (260x10^6) / (4.47x10^9)
=> x = 0.156mg

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