The question is incomplete.
The complete question is: After
decaying for 48 hours, 1/16 of the original mass of a radioisotope sample
remains unchanged. What is the half-life of this radioisotope?
First, calculate how many half-lives have passed to reach 1/16 of the original mass.
Each time that one half-life time passes the mass reduces to half: =>
1 half-life time => 1/2
2 half-life time => 1/4
3 half-life time => 1/8
4 half-life time = > 1/16
Then 4 half-life time correspond to 48 hours, and 1 half-life time corresponds to x:
4 1
---- = -----
48h x
=> x = 48 h * 1 / 4 = 12 h.
Answer: 12 h.
