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An igneous rock now has 2 grams of potassium-40 (parent) and 2 grams of argon-40 (daughter). The half-life for this isotope is 1.25 billion years.

A. How many grams of potassium-40 were in the rock originally?
B. How many half-lives have gone by since the rock formed?
C. How many years have gone by since the rock formed?

1 Answer

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Final answer:

The original amount of K-40 in the rock was 2 grams. Approximately 1.36 half-lives have gone by since the rock formed. Approximately 1.7 billion years have gone by since the rock formed.

Step-by-step explanation:

In order to determine the original amount of potassium-40 (K-40) in the rock, we can compare the amount of K-40 to the amount of argon-40 (Ar-40), which is the decay product of K-40. Since the rock currently has 2 grams of K-40 and 2 grams of Ar-40, we can infer that the original amount of K-40 was also 2 grams.

The number of half-lives that have gone by since the rock formed can be calculated by dividing the age of the rock by the half-life of K-40. In this case, since the half-life is 1.25 billion years and the rock is approximately 1.7 billion years old, we can estimate that about 1.36 half-lives have gone by.

To calculate the number of years that have gone by since the rock formed, we can multiply the number of half-lives by the length of one half-life. Using the estimated number of 1.36 half-lives, we can calculate that approximately 1.7 billion years have gone by since the rock formed.

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