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

60.12 miles

Step-by-step explanation:

Using the calculation formula shown below:

\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