Question

If 110. mg of fluorine-18 is shipped at 8:00 A.M., how many milligrams of the radioisotope are still active after 110 min

Answer 1

54.9 mg of the radioisotope are still active after 110 min.

Step-by-step explanation:

Half-life of F-18 is found to be 109.7 minutes

Rate constant

`$k=\frac{0.693}{t_{(1)/(2)}}=0.00632$`

t = time taken = 110 minutes

`$\ln [A]=\ln [A]_(0)-k t$`

[A] is the final quantity

`[A]_0` is the initial quantity

Plugging the values and solving for [A]

`\\$\ln [A]=\ln (110 m g)-\left(0.00632 \min ^(-1) * 110 \min \right)$\\\\$\ln [A]=4.700-0.6952$\\\\$\ln [A]=4.0048$\\\\$[A]=e^(4.0048)$`

[A] = 54.9 mg is the Answer