Final answer:
Using the half-life formula, we can calculate the remaining mass of a radioactive substance after a certain period. For a 40g sample of radioactive Iodine with an 8-day half-life, after 40 days, 1.25 grams will remain.
Step-by-step explanation:
Calculating Remaining Radioactive Material
To determine how much of a radioactive substance remains after a certain period of time, we use the concept of half-life. The half-life of a substance is the time required for half of the substance to decay. In the case of radioactive Iodine with a half-life of 8.0 days, after one half-life has passed, half of the original material will have decayed.
To calculate the amount remaining after 40 days for an initial 40g sample, we take the following steps:
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- Determine the number of half-lives: 40 days / 8 days/half-life = 5 half-lives.
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- After each half-life, the remaining amount is halved. So after one half-life, 20g remains, then 10g, 5g, 2.5g, and finally 1.25g after five half-lives.
Thus, after 40 days, there will be 1.25 grams left of the original 40g sample of radioactive Iodine.