Final answer:
To find the remaining amount of sodium-24 after 200 hours, divide 130 mg by 2 raised to the power of the number of half-lives passed. With a half-life of 14.96 hours and 200 hours elapsed, more than 13 half-lives have passed, leaving a negligible amount of the original sample.
Step-by-step explanation:
Given a sample of sodium-24 with a half-life of 14.96 hours, you want to calculate how much will remain after 200 hours. The calculation involves using the concept of half-lives, which indicates the time required for half of the radioactive substance to decay. During each half-life period, the amount of substance is reduced by half.
By dividing the total time elapsed (200 hours) by the half-life (14.96 hours), we find the number of half-lives that have passed. For sodium-24, it's approximately 13.37 half-lives. Then we apply the formula to find the remaining amount:
Remaining amount = Initial amount / (2 raised to the power of number of half-lives)
In this case:
Remaining amount = 130 mg / (213.37)
Calculating the power of 2 for 13.37 half-lives gives us a very small fraction, indicating that after 200 hours, a negligible amount of sodium-24 will remain from the original 130 mg sample.