Final answer:
To find the time it takes for 71% of radioactive nuclide 63Ni to decay, we use the first-order decay equation with its half-life of 100 years. The calculation shows that approximately 179 years are needed for 71% to decay.
Step-by-step explanation:
The student's question concerns the time it takes for 71% of a sample of radioactive nuclide 63Ni to decay, which can be solved using the concept of half-life from first-order kinetic processes in nuclear chemistry.
According to its half-life of 100 years, after 100 years, 50% of the nuclide will remain; after 200 years, 25% will remain, and so on. To find how long it takes for 71% of 63Ni to decay instead of a multiple of 50%, we need to use the first-order decay equation:
ln(N/N0) = -kt
where N is the final amount of substance, N0 is the initial amount, k is the decay constant, and t is time. The decay constant k can be determined by the relationship k = ln(2)/t1/2, where t1/2 is the half-life. To calculate the time it takes for 71% to decay, we set N/N0 equal to 0.29 (since 100% - 71% = 29% remaining) and solve for t.
Through calculation, we find that the time needed for 71% to decay is approximately 179 years, which is the closest answer provided in the options given.