To determine how many grams of the parent isotope will be left after 3 half-lives from an initial 16 gram sample, follow these steps:
1. Understand the concept of a half-life: The half-life of an isotope is the time required for half of the isotope in a sample to decay.
2. Determine the initial amount of the isotope: In this case, you start with 16 grams of the isotope.
3. Calculate the number of half-lives: The question specifies that there are 3 half-lives.
4. Apply the process of decay over each half-life:
- After the first half-life: Half of 16 grams remains, which is [tex]\( 16 / 2 = 8 \)[/tex] grams.
- After the second half-life: Half of 8 grams remains, which is [tex]\( 8 / 2 = 4 \)[/tex] grams.
- After the third half-life: Half of 4 grams remains, which is [tex]\( 4 / 2 = 2 \)[/tex] grams.
After 3 half-lives, you will have 2 grams of the parent isotope remaining in the sample.
Therefore, the correct answer is:
A. 2
