It will take 112 years for a 68 mg sample of strontium-90 to decay to a mass of 17 mg.
Step-by-step explanation:
The half-life of strontium-90 is 28 years. To determine how long it will take a 68 mg sample to decay to a mass of 17 mg, we need to calculate the number of half-lives it will take for the mass to decrease from 68 mg to 17 mg.
Each half-life reduces the mass of the radioactive substance to half of its previous value. So, we divide the initial mass (68 mg) by the final mass (17 mg) to find the number of half-lives: 68 mg ÷ 17 mg = 4 half-lives.
Since the half-life of strontium-90 is 28 years, we multiply the number of half-lives by the half-life period to find the total time it will take: 4 half-lives × 28 years = 112 years.