Final answer:
In 24 hours, there are approximately 9.23 half-lives of Mn-56. After 5 half-lives of Mn-56, 0.625 mg of a 20.0 mg sample would remain.
Step-by-step explanation:
Mn-56 decays by beta emission and has a half-life of 2.6 hours. To find out how many half-lives there are in 24 hours, you divide 24 hours by the half-life of 2.6 hours.
24 hours ÷ 2.6 hours/half-life = approximately 9.23 half-lives
Regarding how many milligrams of a 20.0 mg sample remain after 5 half-lives, we can use the following formula:
Amount remaining = Initial amount × (½)^number of half-lives
Amount remaining = 20.0 mg × (0.5)^5
Amount remaining = 20.0 mg × 0.03125
Amount remaining = 0.625 mg
After 5 half-lives, 0.625 mg of the original 20.0 mg sample would remain.