Final answer:
The effective half-life of a radioactive isotope can be calculated by multiplying the physical and biological half-lives and dividing by their sum.
Step-by-step explanation:
The effective half-life of a radioactive isotope is the time it takes for the activity of the isotope to decrease by half, taking into account both its physical and biological decay. In this case, the physical half-life is 6 hours and the biological half-life is 10 hours.
The effective half-life can be calculated by taking the product of the physical and biological half-lives and dividing it by their sum. So the effective half-life = (6 hours × 10 hours) / (6 hours + 10 hours) = 4.28 hours.
Therefore, the effective half-life of the radioactive isotope is 4.28 hours, which is closest to option c. 4.3 hr.