Final answer:
Thorium-234 has a half-life of 24 days. To determine the time it takes for 15 grams of thorium-234 to decay, we need to use the concept of half-lives. Based on the options provided, the closest answer would be C) 12.96 hours.
Step-by-step explanation:
Thorium-234 has a half-life of 24 days. To determine the time it takes for 15 grams of thorium-234 to decay, we need to use the concept of half-lives. The number of half-lives can be calculated by dividing the elapsed time by the half-life of the substance. Since the question does not provide any information about the elapsed time, we can't determine the exact answer. However, we can calculate the number of half-lives for different time options and choose the option where the resulting mass is closest to 0 grams.
A) 3.24 hours: This would be too early for significant decay to occur. B) 6.48 hours: This would still be too early for significant decay to occur. C) 12.96 hours: This would result in around half of the original 15 grams remaining, as it is close to one half-life. D) 25.92 hours: This would result in less than a quarter of the original 15 grams remaining, as it is close to two half-lives. Therefore, based on the options provided, the closest answer would be C) 12.96 hours, where around half (approximately 7.5 grams) of the original 15 grams of thorium-234 would remain after that time.