A 437.7 ng sample of an unknown radioactive substance was placed in storage and its mass measured periodically. After 47 days the amount of radioactive substance had decreased to 54.71 ng.

Question

How many half‑lives of the unknown radioactive substance have occurred?

Answer 1

So Gillian R.,

Just set up the exponential decrease equation and examine it. The substance goes down by ratio, with a half-life decreasing the amount to 0.5 of the original mass. Figure out what mathematical operation describes the inverse operation of an exponential decay. Perform that operation on the ratio you have, and compare the result (some power of 0.5) with 47 days. Good luck. If you think you can avoid the math, think again.

-- Cheers, -Mr. d.

Answer 2

This problem could be harder if it wasn't a nice even increment of a half life.

Since you start with 437.7 ng, after 1 half life, since half of the material will be gone, there will be 437.7/2 or 218.85 ng left.

After 2 half lives, there would be 218.85/2 ng or 109.425 ng left.

After 3 half lives, there would be 109.425/2 ng or 54.7125 ng left, which happens to be what we are looking for.

So 3 half lives have occurred.