Final answer:
To calculate the time elapsed for I-131 decay from 700.00 g to 43.75 g, we find the number of half-lives that fit into this decay process, which is 4, and then multiply it by the half-life period of I-131, which is 8 days, obtaining 32 days. None of the Option is correct.
Step-by-step explanation:
If a sample of I-131 decays from 700.00 g to 43.75 g, we can find out how much time has passed by using the concept of half-lives. Iodine-131 has a half-life of approximately 8 days. To solve this problem, we need to determine how many half-lives have elapsed to get from 700.00 g to 43.75 g.
Let's start by finding how many half-lives it takes for 700.00 g to decay to 43.75 g:
After 1 half-life: 700 g / 2 = 350 g
After 2 half-lives: 350 g / 2 = 175 g
After 3 half-lives: 175 g / 2 = 87.5 g
After 4 half-lives: 87.5 g / 2 = 43.75 g
So, it takes 4 half-lives to decay from 700.00 g to 43.75 g. Now we multiply the number of half-lives by the half-life period of I-131:
Time elapsed = 4 half-lives × 8 days/half-life = 32 days
While 32 days is not one of the multiple choice answers provided, there might have been a mistake in the formulation of the options since none of them match the calculated time. Therefore, based on our calculations and understanding of radioactive decay, the correct answer is not listed among the options.