Final answer:
The half-life of cobalt-60 is 5.27 years as indicated by the provided figures. Over 21.08 years, you would expect the mass of a cobalt-60 sample to reduce to approximately 6.25% of its original mass, which aligns with the decrease from 24 g to 1.5 g in the student's sample.
Step-by-step explanation:
The half-life of cobalt-60 is the time it takes for half of the isotope to decay. According to multiple figures referenced, including Figure 21.10, Figure 20.10, and Figure 11.3.1, the half-life of cobalt-60 is 5.27 years. Therefore, in a period of 21.08 years, you would expect about four half-lives to occur (since 21.08 is approximately four times 5.27). This means that from an initial sample size, you would have 50% after 5.27 years, 25% after 10.54 years, 12.5% after 15.81 years, and approximately 6.25% after 21.08 years. Since the student's cobalt-60 sample decreased from 24 g to 1.5 g over 21.08 years, this reduction is consistent with a substance that has a half-life of 5.27 years, which matches the provided information exactly.