The half-life of a radioisotope is defined as the time required for half of the radioactive nuclei in a sample to decay. This means that, after one half-life, only half of the original amount of the radioisotope remains.
Let’s review the options:
(a) Half the time taken for complete decay: This is incorrect, as half-life does not represent a fraction of the total time for complete decay.
(b) Half the time taken for half the decay: This phrasing is incorrect; it misinterprets the concept of half-life.
(c) Time taken for complete decay: Radioactive decay is a probabilistic process, so it technically never "completes" entirely; there will always be some remaining nuclei.
(d) Time taken for half the decay: This is correct, as half-life specifically refers to the time required for half of the substance to decay.
Correct Answer: (d) Time taken for half the decay