Question

A pure sample of a newly discovered radioactive isotope is discovered. It has a half-life of 78 y. Determine how long until only 1/32 of the original amount remains.

Answer 1

It will take 390 years for a radioactive isotope with a half-life of 78 years to be reduced to 1/32 of its initial amount, based on the calculation of 5 half-lives.

Step-by-step explanation:

When we want to determine how long it will take until only a specific fraction of a radioactive isotope remains, such as 1/32 of the original amount, we need to calculate the number of half-lives that will have passed to reach that fraction. The given half-life is 78 years for the isotope in question. To find out after how many years only 1/32 of the original amount remains, we can use the following procedure:

Therefore, it will take 390 years for the sample to be reduced to 1/32 of its initial amount.