Final answer:
The half-life of radioactive isotopes is the primary factor influencing the storage time of radioactive waste, requiring long-term containment solutions.
Step-by-step explanation:
The factor associated with radioactive waste that has the biggest impact on its storage time is the half-life of the radioactive isotopes contained within the waste. Radioactive isotopes like plutonium-239 have a half-life of 24,000 years, dictating a need for long-term storage.
High-level radioactive waste, such as used nuclear reactor fuel, is in solid form and requires storage in pools of water for cooling and radiation shielding, followed by containment in air-cooled concrete or steel containers. Ultimately, the half-life determines the duration for which the waste remains hazardous and must be safely isolated from the environment.