Final answer:
After three half-lives, 75 undecayed headsium nuclei would remain from an initial sample of 600 nuclei, as the quantity halves with each half-life.
Step-by-step explanation:
The subject of the question is radioactive decay, which involves understanding how the amount of a radioactive substance decreases over time due to its nuclei decaying into other elements or isotopes. Radioactive decay follows an exponential decay pattern, where the amount of substance halves after each half-life. The question asks for the amount of undecayed headsium remaining after three half-lives. Given an initial sample of 600 nuclei, the amount remaining after one half-life would be 300 (half of the initial). After the second half-life, this amount would halve again, resulting in 150 nuclei (half of 300). Finally, after the third half-life, we would be left with half of 150, which is 75 undecayed headsium nuclei.