# Question #b61f8

Mar 19, 2014

At 3:30pm there will be approximately 0.5868mg of fluorine.

The original amount (10.0 mg) is going to be halved every half-life. So, every 110 minutes, the amount is halved. After the first hour, 10mg --> 5mg. Second hour, 5mg --> 2.5mg. And so on.

We have to first figure out how many half-lives are within the time period. From 8:00am to 3:30pm is 7 hours, 30 minutes, or 7.5 hours. To calculate how many hours 110 minutes is, divide by 60 minutes (1 hour) --> $\left(110 \text{min")/(60"min}\right)$ = $1$ $\frac{5}{6}$ hours.

We can figure out the number of half-lives by dividing our total amount of time by the length of a single half-life.
Number of half lives = $\frac{7 \frac{1}{2}}{1 \frac{5}{6}}$ hours = $4$ $\frac{1}{11}$ half lives

Leftover amount: Original amount x ${\left(\frac{1}{2}\right)}^{\text{number of half lives}}$
= 10.0mg x ${\left(\frac{1}{2}\right)}^{4 \frac{1}{11}}$ = 0.5868mg (rounded)