**Problem:**

^{228}Ac has a half life of 6.13 hours. How much of a 5.0 mg sample would remain after one day?

**Solution:**

The first step is to determine the number of half lives that have elapsed.

number of half lives = 1 half life/6.13 hours x 1 day x 24 hours/day

number of half lives = 3.9 half lives

For each half life, the total amount of the isotope is reduced by half.

Amount remaining = Original amount x 1/2

^{(number of half lives)}

Amount remaining = 5.0 mg x 2

^{-(3.9)}

Amount remaining = 5.0 mg x (.067)

Amount remaining = 0.33 mg

**Answer:**

After 1 day, 0.33 mg of a 5.0 mg sample of

^{228}Ac will remain.