Base your answer on the information below. The radioisotope uranium-238 occurs naturally in Earth's crust. The disintegration of this radioisotope is the first in a series of spontaneous decays. The sixth decay in this series produces the radioisotope radon-222. The decay of radon-222 produces the radioisotope polonium-218 that has a half- life of 3.04 minutes. Eventually, the stable isotope lead-206 is produced by the alpha decay of an unstable nuclide. Determine the original mass of a sample of Po-218, if 1.50 milligram of the sample remains unchanged after 9.12 minutes

The half-life of a radioactive material is the time taken for half the amount ofnthe original material present in a radioactive material to decay or disintegrate.

After each half-life, half the original material present at the start remains.

For the radioactive polonium-218 having a half-life of 3.04 minutes, it means that if 1 g is the starting material, after 3.04 minutes, 1/2 g will be remaining; after, 6.08 minutes 1/2 of 1/2 which is 1/4 of the starting material will be remaining; and after 9.12 minutes, 1/2 of 1/4 = 1/8 g will be remaining.

From the question, number of half-lives undergone after 9.12 minutes = 9.12/3.04 = 3 half-lives.

After 3 half-lives, 1/8 of the original material is remaining.

1/8 = 1.50 mg

The original mass of the sample at the start = 1.50 mg × 8 = 12 mg

Therefore, 12 milligrams of Po-218 was the mass of the original starting material.