Final answer:
To determine the time for an 8.00-mg sample of Strontium-90 to decay to 2.00 mg, we calculate the number of half-lives required. Sr-90 has a half-life of 28.8 years, and after two half-lives (57.6 years), the sample would reach the desired 2.00 mg.
Step-by-step explanation:
To calculate the time required for an 8.00-mg sample of Strontium-90 (Sr-90) to decay until only 2.00 mg remains, we can use the concept of half-life. The half-life is the time it takes for half of the sample to decay. According to the provided reference, the half-life of Sr-90 is 28.8 years. To find out how many half-lives are needed for an 8.00-mg sample to reduce to 2.00 mg, we can set up a decay process where with each half-life, the sample's mass halves.
Starting with 8.00 mg, after one half-life, we would have 4.00 mg, and after two half-lives, we would have 2.00 mg. This is exactly the amount we're left with, so that means it takes two half-lives to go from 8.00 mg to 2.00 mg. Therefore, we multiply the number of half-lives by the half-life period:
Time required = 2 × 28.8 years = 57.6 years
So, it will take 57.6 years for the 8.00-mg sample of Sr-90 to decay until only 2.00 mg remains unchanged.