If after 15 years,10 mg of an original 320-mg sample of a radioactive isotope remain,how long is the half-life of this isotope?

Question

Quizplus · Accepted Answer

The half-life can be found using the formula for exponential decay, where the remaining amount of a substance is equal to the initial amount times one-half raised to the power of the number of half-lives that have passed. In this case, 10 mg remains from an original 320 mg, which means the substance has gone through 5 half-lives (since 320 -> 160 -> 80 -> 40 -> 20 -> 10). Given that this takes 15 years, each half-life is 15 years / 5 = 3 years.

If After 15 Years,10 Mg of an Original 320-Mg Sample