Question

If you have a 325 gram sample of a radioactive isotope with a half-life of 10 years, how much of the isotope will you have left after 40 years?

Answer 1

After 40 years, which is four half-lives of the radioactive isotope with a 10-year half-life, there will be approximately 20.3125 grams of the isotope left from an original sample of 325 grams.

Step-by-step explanation:

The question relates to the concept of radioactive decay and specifically the calculation of the remaining amount of a radioactive isotope after a certain number of half-lives have passed. To find out how much of the isotope will be left after 40 years, use the half-life formula. The given half-life of the isotope is 10 years. Therefore, after 40 years, which encompasses four half-lives, the amount of radioactive isotope remaining can be calculated as follows:

First half-life (10 years): 325 g / 2 = 162.5 g
Second half-life (20 years): 162.5 g / 2 = 81.25 g
Third half-life (30 years): 81.25 g / 2 = 40.625 g
Fourth half-life (40 years): 40.625 g / 2 = 20.3125 g

So, after 40 years, you will have approximately 20.3125 grams of the original radioactive isotope left.