How do half-lives work.?

Question

in this problem.

(a 160g sample of radium-223 decays to 2.5 grams after 72 days. What is the half life of Radium-223?)

Answer 1

A half-life is the amount of time it takes for half the atoms of any given radioactive sample to decay. With an original sample of 160 grams, it must halve six times to decay to 2.5 grams. (160 -> 80 -> 40 -> 20 -> 10 -> 5 -> 2.5). If it does that in 72 days, then one half life is 72/6 or 12 days.