Calculating remaining radioactivity

The half-life decay of radioactive isotopes is not linear. For example, you can’t find the remaining amount of an isotope at 7.5 half-lives by finding the midpoint between 7 and 8 half lives.

If you want to find times or amounts that are not associated with a simple multiple of a half-life, you can use this equation:

In the equation, ln stands for the natural logarithm (the base e log, not the base 10 log; it’s that ln button on your calculator, not the log button). No is the amount of radioactive isotope that you start with (in grams, as a percentage, in the number of atoms, and so on), N is the amount of radioisotope left at some time (t), and t1/2 is the half-life of the radioisotope. If you know the half-life and the amount of the radioactive isotope that you start with, you can use this equation to calculate the amount remaining radioactive at any time.