Question

The equation gives the mass, m, of a radioactive substance remaining after h half-lives. Iron has a half-life of 2.7 years. Which equation gives the mass of a 200 mg iron sample remaining after y years, and approximately how many milligrams remain after 12 years?

1) 1.7 mg
2) 30.8 mg
3) 3.2 mg
4) 9.2 mg

Answer 1

To calculate the remaining mass of a radioactive substance after a certain number of years, you use the radioactive decay formula incorporating the substance's half-life. For an iron sample with a 2.7-year half-life, after 12 years, approximately 30.8 mg would remain from an initial 200 mg.

Step-by-step explanation:

To find the mass of a 200 mg iron sample remaining after y years, we will use the equation for radioactive decay: m = m0(1/2)y/t1/2, where m is the final mass, m0 is the initial mass, y is the time in years, and t1/2 is the half-life of the substance.

For iron with a half-life of 2.7 years, the equation becomes m = 200(1/2)y/2.7. To find how much remains after 12 years, we plug the values into the equation: m = 200(1/2)12/2.7. Calculating this gives us approximately 30.8 mg.