The half-life of xe-133 is 126 hours. Starting with 250 mg, after 500 hours around how many mg remain?
see other post.
To determine the amount of Xe-133 remaining after 500 hours, we can use the concept of half-life.
The half-life of a radioactive substance is the time it takes for half of the initial quantity to decay. In this case, the half-life of Xe-133 is 126 hours.
First, let's find out how many half-lives have passed during the 500 hours. We can do this by dividing the elapsed time (500 hours) by the half-life (126 hours):
Number of half-lives = elapsed time / half-life
= 500 hours / 126 hours
≈ 3.968
Since we cannot have a fraction of a half-life, we take the whole number part of 3.968, which is 3. This means that approximately 3 half-lives have elapsed during the 500 hours.
Next, we can calculate the amount of Xe-133 remaining after 3 half-lives. Every half-life reduces the quantity by half, so after 3 half-lives, we are left with:
Remaining quantity = initial quantity * (1/2)^number of half-lives
= 250 mg * (1/2)^3
= 250 mg * (1/8)
= 31.25 mg
Therefore, after 500 hours, approximately 31.25 mg of Xe-133 would remain.