The half-life of Xe-133 is 126 hours. Starting with 250. mg, after 500 hours around how many mg remain?

A. 63
B. 16
C. 32
D. 125

To determine the amount of Xe-133 remaining after 500 hours, we can use the concept of half-life.

The half-life of Xe-133 is given as 126 hours, which means that in every 126 hours, half of the Xe-133 atoms would decay.

We can calculate the number of half-lives that have occurred during the 500 hours by dividing 500 by 126:

500 hours / 126 hours = 3.97 (approx)

Since we cannot have a fraction of a half-life, we can consider that three half-lives have occurred during the 500 hours.

Each half-life reduces the amount of Xe-133 to half its previous amount. So, after three half-lives, the remaining amount can be calculated as:

Remaining amount = Initial amount × (1/2)^Number of half-lives

Given that the initial amount is 250 mg:

Remaining amount = 250 mg × (1/2)^3
Remaining amount = 250 mg × (1/8)
Remaining amount = 31.25 mg (approx)

Therefore, after 500 hours, approximately 31.25 mg of Xe-133 remain.

Comparing the remaining amount to the given answer choices, we find that the closest option is C. 32 mg, which is approximately equal to 31.25 mg.