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Answer :
Answer:
2.6 billion years old
Explanation:
Initial:
100% k-40
0% ar-40
After 1.3 billion years:
50% k-40
50% ar-40
After 2.6 billion years:
25% k-40
75% ar-40
So the rock is 2.6 billion years old.
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Final answer:
The age of the rock determined through potassium-argon dating is 2.6 billion years, as it contains 25% K-40 and 75% Ar-40 and K-40 has a half-life of 1.3 billion years.
Explanation:
To determine the age of the rock using potassium-argon dating, we apply our understanding of radioactive decay and the concept of half-lives. Given that the rock sample contains 25% K-40 and 75% Ar-40, we know that three-quarters of the original K-40 has decayed into Ar-40. Since potassium-40 (K-40) has a half-life of 1.3 billion years, this means that two half-lives have passed to leave us with a quarter of K-40. Therefore, the age of the rock is 2 half-lives, which is 2.6 billion years old (1.3 billion years per half-life times 2).
