Question

A rock contains 0.257 mg of lead-206 for every milligram of uranium-238. The half-life for the decay of uranium-238 to lead-206 is 4.5 × 10^9 yr. How old is the rock? (show your solution)​

Answer 1

Answer:

Let's assume that the rock contains 1.000 mg of uranium-238 at present. The amount of uranium-238 in the rock when it was first formed therefore equals 1.000 mg plus the quantity that decayed to lead-206. We obtain the latter quantity by multiplying the present mass of lead-206 by the ratio of the atomic mass of uranium to that of lead, into which it has decayed. The total original PM21073 was thus

PM21074

PM21075

Using Equation 21.20, we can calculate the decay constant for the process from its half-life:

PM21076

Rearranging Equation 21.19 to solve for time, t, and substituting known quantities gives

PM21077

Explanation:

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