Final answer:
After 14 years, two half-lives of the radioactive substance will have passed, leaving one-quarter (4g) of the initial 16g. One additional year beyond this point would result in slightly less than 4g remaining, assuming a constant rate of decay.
Step-by-step explanation:
If a student starts with 16g of a radioactive substance and after 7 years only 8g remain, we can establish that the half-life of this substance is 7 years. The amount of radioactive substance remaining after a certain amount of time can be calculated using the concept of half-life, which is the period it takes for half of the substance to decay into its daughter elements. The question is to determine how much of the substance will be present after 15 years.
To solve this, we note that after the first half-life (7 years), the substance will be reduced to half its original amount. Consequently, after 14 years (which is two half-lives), the quantity of the substance would be halved twice, leaving one-quarter of the initial amount. Therefore, after 15 years, which is slightly more than two half-lives, the amount of substance remaining would be somewhat less than one quarter of the original 16g.
Following the pattern of radioactive decay, we halve the initial amount for each half-life period that passes:
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- After 7 years (1 half-life): 16g / 2 = 8g
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- After 14 years (2 half-lives): 8g / 2 = 4g
Since the question asks for the amount after 15 years, which is 1 year after the second half-life, we need to estimate the decay for that additional year.
Assuming a constant rate of decay, we would take a bit less than the 4g calculated for 14 years to account for the one additional year of decay. Without precise decay rate calculations for each year, the exact amount cannot be determined. However, the expected amount would be just under 4 grams after 15 years.