Fluorine-18, which has a half-life of 110 min, is used in PET scans. b. If 100. mg of fluorine-18 is shipped at 8:00 a.m., how many milligrams of the radioisotope are still active when the sample arrives at the radiology laboratory at 1:30 p.m.?

Verified step by step guidance

1. Determine the total time elapsed from 8:00 a.m. to 1:30 p.m. in minutes.
2. Calculate the number of half-lives that have passed by dividing the total time elapsed by the half-life of fluorine-18.
3. Use the formula for radioactive decay: $N=N_0\times (\frac{1}{2}{)}^n$, where $N_0$ is the initial amount, $n$ is the number of half-lives, and $N$ is the remaining amount.
4. Substitute the initial amount (100 mg), the number of half-lives calculated, and solve for $N$.
5. Interpret the result to find out how many milligrams of fluorine-18 remain active at 1:30 p.m.

Key Concepts

Half-Life

Half-life is the time required for half of the radioactive substance to decay. In the case of Fluorine-18, which has a half-life of 110 minutes, this means that after 110 minutes, only 50 mg of the original 100 mg will remain active. Understanding half-life is crucial for calculating the remaining quantity of a radioactive isotope over time.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This process occurs at a predictable rate, characterized by the half-life. For Fluorine-18, the decay leads to a decrease in the amount of active substance, which is essential for determining how much remains after a specific period.

Exponential Decay Formula

The exponential decay formula is used to calculate the remaining quantity of a radioactive substance over time. It is expressed as N(t) = N0 * (1/2)^(t/T), where N0 is the initial quantity, t is the elapsed time, and T is the half-life. This formula allows for precise calculations of how much Fluorine-18 remains after the time interval from shipment to arrival.