Fluorine-18 is a radioisotope widely used in positron emission tomography to investigate brain activity.The half-life is 109.8 minutes.How long will it take for 2.75 μg of ¹⁸F to decay to 500 ng?

Question

Quizplus · Accepted Answer

To find the time it takes for 2.75 μg of Fluorine-18 to decay to 500 ng, we first convert the initial and final amounts to the same unit (micrograms, μg). 500 ng is equal to 0.5 μg. The half-life formula is used to calculate the decay time: $t = \frac{\ln(\frac{N_0}{N})}{\lambda}$, where $N_0$ is the initial amount, $N$ is the final amount, and $\lambda$ is the decay constant. The decay constant $\lambda$ can be found from the half-life $T_{1/2}$ using $\lambda = \frac{\ln(2)}{T_{1/2}}$. Given the half-life of 109.8 minutes, we can calculate the time it takes for the substance to decay from 2.75 μg to 0.5 μg. The calculation involves logarithms and the known half-life, leading to a result of approximately 270 minutes.

Fluorine-18 Is a Radioisotope Widely Used in Positron Emission Tomography