If you obtained a sample of rock from Venus and determined the abundances of ²³⁸U and ²⁰⁷Pb in it,and found that for every 1 uranium atom there were 3 lead atoms,then what would the age of this rock be? Note that ²³⁸U decays to ²⁰⁷Pb with a half-life of 700 million years.Assume that there was no ²⁰⁷Pb in the rock when it originally formed. A) 1.4 billion years B) 2.8 billion years C) 230 million years D) 4.5 billion years

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Quizplus · Accepted Answer

The age of the rock can be calculated using the formula:t = (ln(N_Pb/N_U)) / (λ)where:t is the age of the rockN_Pb is the number of lead atomsN_U is the number of uranium atomsλ is the decay constantIn this case, we have:N_Pb/N_U = 3λ = ln(2) / (700 million years) = 9.85 x 10^-10 years^-1Substituting these values into the formula, we get:t = (ln(3)) / (9.85 x 10^-10 years^-1) = 1.4 billion yearsTherefore, the age of the rock is 1.4 billion years.

If You Obtained a Sample of Rock from Venus and Determined