Final answer:
After three half-lives of phosphorus-32, which has a half-life of 14.29 days, one-eighth of the original sample remains, so in the case of a 2.4 mg sample, 0.3 mg would be left.
Step-by-step explanation:
The question relates to the concept of radioactive decay and specifically the calculation of the remaining amount of a radioactive isotope after a certain number of half-lives. In the case of phosphorus-32 with a half-life of 14.29 days, after three half-lives, the amount of phosphorus-32 remaining would be one-eighth of the original amount because the substance halves in quantity after each half-life.
For a sample that initially contains 2.4 mg of phosphorus-32, the remaining mass after one half-life would be 1.2 mg, after the second half-life it would be 0.6 mg, and after the third half-life, it would be 0.3 mg.