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A material originally contained 300 kg of uranium-235. The material now contains 281 kg of lead-207. Assuming that all the lead-207 came from the uranium-235, how old is the material?

Answer :

Final answer:

The age of the material is approximately 3.472 billion years.

Explanation:

To determine the age of the material, we can use radioactive dating principles. Uranium-235 decays into lead-207 with a half-life of 0.704 Gyr. Since all the lead-207 in the material came from the uranium-235, we can calculate the number of half-lives that have passed.

First, we need to find the amount of uranium-235 that has decayed. The difference between the original mass (300 kg) and the present mass (281 kg) is 19 kg. Each half-life reduces the amount of uranium-235 by half, so we divide the difference by the initial mass (300 kg) to find the fraction of uranium-235 that remains: 19 kg / 300 kg = 0.0633.

Next, we use the half-life equation (Nt = N0 * (1/2)^(t/h)) to solve for t, the number of half-lives. Rearranging the equation, we have t = (log(Nt) - log(N0)) / log(1/2). Substituting the values, we have t = (log(0.0633) - log(1)) / log(1/2) = 4.939 half-lives.

Since each half-life is 0.704 Gyr, the age of the material is 4.939 * 0.704 Gyr = 3.472 Gyr.

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