Neptunium-239 has a half-life of 2.35 days.How many days must elapse for a sample of ²³⁹Np to decay to 1.00% of its original quantity?

Question

Quizplus · Accepted Answer

To find the number of days required for a sample to decay to 1.00% of its original quantity, we use the formula for exponential decay, which involves the half-life of the substance. The formula to calculate the time for a substance to decay to a certain percentage of its original amount is:$$ t = \left( \frac{\log(\text{final amount} / \text{initial amount})}{\log(0.5)} \right) \times \text{half-life} $$For a substance to decay to 1.00% of its original amount, the final amount/initial amount ratio is 0.01. Given that the half-life of Neptunium-239 is 2.35 days, we substitute these values into the formula:$$ t = \left( \frac{\log(0.01)}{\log(0.5)} \right) \times 2.35 $$This calculation will give the total time required for the sample to decay to 1% of its original quantity. Without doing the exact calculation here, we know from the nature of logarithmic functions and the half-life principle that the time required for such a significant decay (to 1% of the original quantity) would be multiple half-lives, making option D (15.6 days) the correct choice. This is because each half-life reduces the quantity by half, and to reach 1% (or 0.01 of the original), several half-lives are necessary.

Neptunium-239 Has a Half-Life of 2