fluorine-18 half life of 110 min if 100mg was shipped at 8:00 am how many mg are still active at 1;30 pm same day
k = 0.693/t1/2
Substitute k into the equation below.
ln(No/N) = kt
No = 100 mg
You solve for N.
k from above.
t is time from 8:00 am to 1:30 pm but if you substitute half life in minutes, t must be converted to minutes, also.
To determine how many milligrams of fluorine-18 are still active at 1:30 pm, we need to calculate the amount remaining after a certain number of half-lives have passed.
The half-life of fluorine-18 is given as 110 minutes. This means that every 110 minutes, half of the fluorine-18 will decay or become inactive.
From 8:00 am to 1:30 pm, there is a total of 5.5 hours, or 330 minutes.
To find out how many half-lives have occurred in this time period, divide the total time by the half-life:
Number of half-lives = Total time / Half-life
= 330 min / 110 min
= 3
Now, we can calculate the amount of fluorine-18 remaining after three half-lives:
Remaining amount = Initial amount * (1/2)^(Number of half-lives)
The initial amount shipped was 100 mg, so:
Remaining amount = 100 mg * (1/2)^3
= 100 mg * (1/2)^3
= 100 mg * (1/8)
= 12.5 mg
Therefore, at 1:30 pm, the amount of fluorine-18 remaining would be 12.5 mg.