To determine the age of the object based on the remaining percentage of radioactive atoms, we can use the concept of half-lives.
If 12.5% of the radioactive atoms remain, this means that 87.5% of the atoms have decayed.
12.5% is equal to \( \frac{1}{8} \) of the original amount.
Since each half-life reduces the amount of radioactive atoms by half, we can express the remaining amount in terms of half-lives:
- 1 half-life: \( \frac{1}{2} \) of the original amount remains.
- 2 half-lives: \( \frac{1}{4} \) of the original amount remains.
- 3 half-lives: \( \frac{1}{8} \) of the original amount remains.
Thus, it takes 3 half-lives to go from 100% to 12.5%.
Given that one half-life is 800 years, we can multiply: \[ 3 \text{ half-lives} \times 800 \text{ years/half-life} = 2400 \text{ years} \]
Thus, the age of the object is 2400 years. However, since 2400 years isn't listed in the multiple choice options (which seem to be incorrect), we can confirm that:
a. 6400 years
b. 3200 years
c. 1600 years
None of these is correct based on the calculation.
Please verify the question or confirm the choices provided.
1 answer