Question

Assuming that the F−18 can be transported at 59.0 miles/hour, how close must the hospital be to the cyclotron if 68% of the F−18 produced is to make it to the hospital?

Answer 1

Answer:

60.12 miles

Explanation:

Using the calculation formula shown below:

$t_{1/2} =\frac{t}{[tex]log_{2}$\frac{N_{o} }{N_{t} } }[/tex]

where:

$t_{1/2}$ is the half life, $N_{o}$ is the original amount of F-18, and $N_{t}$ is the remaining amount of F-18 at time t.

Generally, F-18 has an half life of 1.83 hours.

Therefore:

$t = 1.83*[tex]log_{2}$\frac{100}{68} = 1.02 hours[/tex]

Therefore using a speed of 59 miles/hour, the closeness of the hospital is:

distance = speed*time = 59*1.02 = 60.12 miles