Final answer:
After 80 hours, four half-lives have occurred for a radioactive isotope with a 20-hour half-life, so the correct answer is d. 4.
Step-by-step explanation:
If a radioactive isotope has a half-life of 20 hours, then after 80 hours have passed, four half-lives have occurred because 80 divided by 20 equals 4. So, the correct answer to how many half-lives have occurred after 80 hours have passed is d. 4.
The concept of half-life is crucial to understand radioactive decay. The half-life is the time it takes for half of the isotopes in a sample to decay. This means after one half-life, you have 50% of your original sample, after two half-lives, 25%, and this process continues with each successive half-life.