Fluorine-18, which has 1/2 life of 110 minutes, is used in PET scans. If 100 mg of fluorine-18 is shipped @8AM, how many milligrams of the radioisotope are still active if the sample arrives at the lab at 1:30 pm?
k = 0.693/t1/2
ln(No/N) = kt
No = 18 mg
N = unknown
k from above.
t = minutes from 8 am to 1:30 pm.
OR, to keep the numbers a little more workable, you may wish to use t1/2 in hours (110/60), then use t = hours from 8:00 AM to 1/:30 pm.
0.50
To determine how many milligrams of fluorine-18 are still active when it arrives at the lab at 1:30 pm, we need to calculate the amount of decay that has occurred during the shipping time.
The half-life of fluorine-18 is 110 minutes, which means that after 110 minutes, half of the radioactive substance will decay.
Given that the sample is shipped at 8 AM and arrives at 1:30 pm, we need to calculate the time difference between the two.
8 AM to 1:30 pm is a time difference of 5 hours and 30 minutes (or 330 minutes), as there are 60 minutes in an hour.
Now, let's determine how many half-lives have passed during this time. We can divide the time difference (330 minutes) by the half-life (110 minutes):
330 minutes / 110 minutes = 3
Three half-lives have passed during the shipping time.
Each half-life reduces the quantity of the substance by half. So, after three half-lives, the quantity will be reduced by a factor of 2^3 = 8.
Therefore, to determine the remaining amount of fluorine-18, we can multiply the initial quantity (100 mg) by the fraction 1/8, since it has undergone three half-lives:
100 mg * 1/8 = 12.5 mg
So, if 100 mg of fluorine-18 is shipped at 8 AM and arrives at the lab at 1:30 pm, then approximately 12.5 mg of the radioisotope will still be active.