The half-life of a certain radioactive element is 800 years. How old is an object if only 12.5% of the radioactive atoms in it remain?

Question

a
1600 years
b
6400 years
c
3200 years

Answer 1

To find the age of the object when only 12.5% of the radioactive atoms remain, we can use the concept of half-lives.

If 12.5% of the radioactive atoms remain, that means the object has gone through several half-lives. Specifically:

1. After 1 half-life (800 years), 50% remains.
2. After 2 half-lives (1600 years), 25% remains.
3. After 3 half-lives (2400 years), 12.5% remains.

Thus, the object is 2400 years old. However, this option isn’t listed in the choices you provided (1600, 6400, 3200 years).

To clarify further in case of an error in the calculation:

• 12.5% corresponds to \( \frac{1}{8} \), indicating that the element has gone through 3 half-lives (since \( \frac{1}{2} \to \frac{1}{4} \to \frac{1}{8} \)).

Calculating the total time for 3 half-lives:

• \( 3 \times 800 = 2400 \) years.

Since 2400 years was not an option and might've been overlooked, please ensure you provided all choices correctly. Based on the information available, the answer is 2400 years. If using the provided options, none are correct.