Answer
At 1:30 PM, only 12.5 mg of the radioisotope are still active.
Work Step by Step
1. Calculate the number of half-lives.
Between 8:00 and 12:00, there are 4 hours.
$4 h \times \frac{60 min}{1h} = 240 min$
Between 12:00 AM and 1:30 PM, there is 1 hour and 30 minutes.
1 h and 30 min = 60 min + 30 min = $90 min$
Total time: $240 min + 90 min = 330 min$
$330 min \times \frac{1half-life}{110 min} = 3 half-lives$
2. Now, calculate the remaining mass after 3 half-lives:
1 Half-Life: $100.mg \times \frac{1}{2} = 50.0 mg$
2 Half-Lives: $50.0 mg \times \frac{1}{2} = 25.0 mg$
3 Half-Lives: $25.0 mg \times \frac{1}{2} = 12.5 mg$
