Question

a rock sample contains 25 percent k-40 and 75 percent daughter product ar-40. if k-40 has a half-life of 1.3 billion years, how old is the rock?

Answer 1

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.

Step-by-step 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).

Answer 2

2.6 billion years old

Step-by-step 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.