To determine the age of the object based on the percentage of radioactive atoms remaining, we can use the concept of half-lives.
The half-life of the element is 800 years, meaning every 800 years, half of the radioactive atoms will decay.
If only 12.5% of the radioactive atoms remain, we can express this in terms of half-lives:
- 100% of the original amount decays to 50% after 1 half-life (800 years).
- 50% decays to 25% after 2 half-lives (1600 years).
- 25% decays to 12.5% after 3 half-lives (2400 years).
Therefore, if 12.5% of the radioactive atoms remain, the object is 3 half-lives old:
\[ 3 \times 800 \text{ years} = 2400 \text{ years} \]
So the age of the object is 2400 years.
Since this answer is not amongst the choices given (A) 1600 years, (B) 6400 years, or (C) 3200 years, let's make sure to summarize correctly; we are looking for the age of the object with 12.5% remaining.
If we also want to check:
If 100% = 0 half-lives, then after:
- Half-life 1 = 50%
- Half-life 2 = 25%
- Half-life 3 = 12.5%
It confirms that after 2400 years (not provided in the options) only 12.5% of radioactive atoms remain. So, none of the options presented match the correct answer of 2400 years.
Nonetheless, if you needed other calculations or needed more specific help, do let me know!