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.