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A radioactive substance has a half life of 5 million years. What is the age of a rock in which 25% of the original radioactive atoms remain?

User CJ Teuben
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Step-by-step explanation:

If a radioactive substance has a half-life of 5 million years, it means that after every 5 million years, the amount of radioactive atoms remaining is reduced by half.

Since we want to find the age of a rock where 25% of the original radioactive atoms remain, it means that 75% of the original atoms have decayed.

To find the number of half-lives that have occurred, we can use the equation:

n = (log(N₀ / N) / log(2))

Where:

- n is the number of half-lives

- N₀ is the initial number of atoms

- N is the remaining number of atoms

In this case, we know that N is 25% of N₀, so N/N₀ = 0.25.

Plugging this into the equation, we have:

n = log(1 / 0.25) / log(2)

n = log(4) / log(2)

n ≈ 2

This means that two half-lives have occurred, as after two half-lives, 25% of the original radioactive atoms will remain.

Since each half-life is 5 million years, the age of the rock can be calculated by multiplying the number of half-lives by the half-life duration:

Age = 2 * 5 million years

Age = 10 million years

Therefore, the age of the rock is 10 million years.

User Sameera Jayasoma
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