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In a sample of rock, it is found that 20% of the uranium-238 has decayed into lead-206. Using the graph on page 253, estimate the age of the rock if the half-life of uranium-238 is 4.47 Billion years.​

User Tertium
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Answer: 20.9 billion years.

Explanation: To estimate the age of the rock, we can use the fact that the half-life of uranium-238 is 4.47 billion years. This means that half of the uranium-238 in the rock would have decayed into lead-206 after 4.47 billion years, and half of what remains would decay in the next 4.47 billion years, and so on.

If 20% of the uranium-238 in the rock has decayed into lead-206, then 80% of the original uranium-238 is still present in the rock. This means that the rock has gone through one half-life of uranium-238 decay, and we can estimate its age by using the graph on page 253.

According to the graph, the ratio of lead-206 to uranium-238 after one half-life is approximately 0.027. This means that the rock contains 0.027 times as much uranium-238 as it did originally, and the remaining 80% of the uranium-238 corresponds to 0.8 times the original amount.

Therefore, we can estimate the original amount of uranium-238 in the rock as follows:

Original amount of uranium-238 = (0.8) / 0.027 = 29.63 times the current amount

Next, we can use the fact that each half-life corresponds to a reduction in the amount of uranium-238 by a factor of 2, to estimate the number of half-lives that have passed since the rock formed:

Number of half-lives = log2(29.63) = 4.88

Finally, we can estimate the age of the rock as follows:

Age of the rock = (4.88) x (4.47 billion years per half-life) = 20.9 billion years

Therefore, we can estimate that the age of the rock is approximately 20.9 billion years.

User Vek
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