Strontium-90 is a radioactive waste product from nuclear reactors. It has a half-life of 29 years. How many years will it take for a quantity of strontium-90 to decay to 1/16 (one-sixteenth) of its original mass?
since 1/16 = (1/2)^4
It will take 4 half-lives to decay that far.
To determine how many years it will take for a quantity of strontium-90 to decay to 1/16 of its original mass, we can use the concept of half-life.
The half-life of strontium-90 is 29 years, which means that in 29 years, half of the original quantity of strontium-90 will have decayed. After another 29 years, half of the remaining strontium-90 will decay, and so on.
Since we want to find the time it takes for strontium-90 to decay to 1/16 of its original mass, we need to determine how many half-lives it will take to reach this point.
Let's start by finding the number of halvings required to get from the original mass to 1/16 of the original mass.
1/2 (1 half-life) --> 1/4 (2 half-lives) --> 1/8 (3 half-lives) --> 1/16 (4 half-lives)
Therefore, it will take 4 half-lives for the quantity of strontium-90 to decay to 1/16 of its original mass.
Since the half-life of strontium-90 is 29 years, we can calculate the total time required by multiplying the half-life by the number of half-lives:
Total time = Half-life x Number of half-lives
Total time = 29 years x 4 half-lives
Total time = 116 years
Therefore, it will take 116 years for a quantity of strontium-90 to decay to 1/16 of its original mass.