Question

10 grams of calcium-37 remain after 700 milliseconds (0.700 seconds).

How much calcium was in the original sample?""

Please calculate and provide the amount of calcium that was in the original sample before the decay.

Answer 1

To calculate the original amount of calcium, the half-life concept is used. However, the exceedingly large number of half-lives calculated within 0.700 seconds is not realistic, indicating a potential issue with the decay time or half-life provided.

Step-by-step explanation:

To calculate the original amount of calcium in the sample, we need to use the concept of half-life, which is the time required for half of a sample of a radioactive substance to decay. The provided half-life of calcium-37 is 1.78 milliseconds (ms). Since we know 10 grams remain after 700 ms, we can calculate the number of half-lives that have passed using the formula number of half-lives = time elapsed / half-life. Then, by using the formula initial amount =
`remaining amount x (2^(number of half-lives))`, we can determine the original amount of calcium.

First, calculate the number of half-lives that have passed:
number of half-lives = 0.700 s / 0.00178 s = 393.258426966

Now, using the initial amount formula:
initial amount =
`10 g x (2^(393.258426966))`

Given that the number of half-lives is not a whole number, this problem involves estimating the amount remaining after a non-integer number of half-lives. However, practically, since the number of half-lives is exceedingly large, the initial amount of calcium would be incredibly large and not realistic due to the limitations of mass and matter. Therefore, we can conclude that there has been a mistake in the calculation or understanding of the decay process as no realistic sample could have such a high number of half-lives within such a short time span. This suggests that the time elapsed or half-life provided might not be accurate for a real-world scenario.