A 71 mg sample of a radioactive nuclide is administered to a patient to obtain an image of her thyroid. If the nuclide has a half-life of 12 hours, how much of the nuclide remains in the patient after 4.0 days?
How many half lives is that? ANS: 8
71mg (1/2)^8= (use your calculator)
To find out how much of the nuclide remains in the patient after 4.0 days, we can use the concept of half-life and exponential decay.
The given half-life of the nuclide is 12 hours, which means that after every 12 hours, the amount of the nuclide is reduced by half.
First, let's convert the 4.0 days into hours. Since there are 24 hours in a day, we have:
4.0 days * 24 hours/day = 96 hours
Now, we need to figure out how many half-lives have passed during this time. We can do that by dividing the total time (96 hours) by the half-life (12 hours):
96 hours / 12 hours/half-life = 8 half-lives
So, after 4.0 days (96 hours), there have been 8 half-lives of the nuclide.
To calculate the amount of the nuclide remaining, we can use the formula:
Remaining amount = Initial amount * (1/2)^(number of half-lives)
The initial amount is given as 71 mg. Plugging in the values, we get:
Remaining amount = 71 mg * (1/2)^8
Calculating this expression:
Remaining amount = 71 mg * (1/256)
Remaining amount ≈ 0.27734 mg
Therefore, after 4.0 days, approximately 0.27734 mg of the nuclide remains in the patient.