Question

Iodine-126, a y(gamma ray)-emitter, has a half life of 13.3h. If a diagnostic dose is 10ng, how much is left after 2.5 days?

I got 44.19. is that correct??

Answer 1

Nope. Remember a couple of things, that you're given a dose of 10 nanograms, your half life is given in units of hours and your amount of time is asking in days. Since it is decaying, you have a negative rate, and rate is related to half life by the formula k=ln2/halflife.

Answer 2

another way of thinking about half lives is to ask "how many half-lives will pass over 2.5 days?" 2.5 days is 60 hours. 60 hours is 4.5 half-lives. What's left of the original smaple will have been "cut in half" between 4 and 5 times over the course of 2.5 days.

Answer 3

Yeah, most half-life problems are complicated more by doing calculations. Often you can just look at it and think, ok, so if this is how much is left after so much time, how many times am I half-ing the original amount?