Plutonium-239 \(\left(t_{1 / 2}=2.41 \times 10^{4} \mathrm{yr}\right)\) represents a serious nuclear waste hazard. If seven half-lives are required to reach a tolerable level of radioactivity, how long must \({ }^{239}\) Pu be stored?

Radioactive decay is a natural process where unstable atomic nuclei lose energy by emitting radiation. This process changes the atom into a different element or a different isotope. It's a step-by-step transformation, shedding particles and energy over time.

Every radioactive isotope decays at a specific rate, which is unique to each kind. This is why knowing the decay rate or half-life of an isotope is crucial. The decay process continues until a stable, non-radioactive isotope is formed. Radioactive decay is spontaneous and cannot be sped up or slowed down by external factors like temperature or pressure.

In simpler terms, think of it as a clock that ticks away the unstable particles, making them stable over a period. For educational purposes, understanding radioactive decay helps us grasp how long certain materials remain hazardous and informs us about measures for safe handling and disposal.

Dealing with nuclear waste is a critical issue for both environmental safety and human health. Nuclear waste management involves the processes of collecting, transporting, processing, storing, and disposing of radioactive materials.

The challenge with nuclear waste like Plutonium-239 is its long half-life, which makes it dangerously radioactive for thousands of years. Effective waste management strategies include storing the waste in secure facilities designed to contain radiation and isolate it from the environment.

Storage solutions include:

• Deep geological repositories: Storing waste deep underground to ensure isolation from living organisms.
• Dry cask storage: Using reinforced containers that are durable and designed to resist environmental hazards.

The goal of nuclear waste management is to minimize the exposure to radiation and protect both the environment and public health.

Calculating the half-life of a radioactive isotope is essential to predicting its decay pattern over time. The half-life (symbolized as \(t_{1/2}\)) is the time taken for half the quantity of a radioactive isotope to decay.

For Plutonium-239, we are given that \(t_{1/2} = 2.41 \times 10^{4} \text{ years}\). If we need to determine how long it takes for the radioactivity to reach a tolerable level, requiring seven half-lives, the calculation is straightforward. Multiply the isotope's half-life by the number of half-lives: \[ \text{Total time} = 7 \times t_{1/2} \] Substituting in the given half-life, we get: \[ \text{Total time} = 7 \times 2.41 \times 10^{4} \text{ years} = 1.687 \times 10^{5} \text{ years} \] This means Plutonium-239 must be stored for approximately 168,700 years to decay to a tolerable level.

Understanding half-life calculations allows us to manage radioactive materials more effectively and plan long-term storage solutions, ensuring safety for future generations.