7. Your rock sample's parent isotope has a half-life of 250 million years, If the sample contains 25% parent and 75% daughter, how old is the rock?

Age of rock = 500 million years

Explanation:

The age of the rock can be calculated by determining the number of decays (half-lives) the parent rock has undergone.

The half-life of a radioactive material is the time it takes for half the the quantity present in that material to decay or disintegrate.

The half-life of the rock sample = 250 million years

Amount of parent rock left in the rock sample = 25% = 1/4

Number of half-lives, n required is given as (1/2)ⁿ

Number of half-lives undergone by the parent rock sample to be 1/4 of the original sample is given as:  (1/2)ⁿ = 1/4

1/4 = (1/2)²

Therefore, n = 2

Age of rock = number of half-lives * half-life (in years)

Age of rock = 2 * 250 million years

Age of rock = 500 million years

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