In addition to being used to generate commercial electricity, nuclear reactors are used in government-sponsored research and development programs, universities and industry; in science and engineering experimental programs; at nuclear weapons production facilities; and by the U.S. Navy and military services. The operation of nuclear reactors results in spent reactor fuel. The reprocessing of that spent fuel produces high-level radioactive waste (HLW).

The fuel for most nuclear reactors consists of pellets of ceramic uranium dioxide that are sealed in hundreds of metal rods

Alpha decay is usually restricted to the heavier elements in the periodic table. (Only a handful of nuclides with atomic numbers less than 83 emit an -particle.) The product of -decay is easy to predict if we assume that both mass and charge are conserved in nuclear reactions. Alpha decay of the 238U "parent" nuclide, for example, produces 234Th as the "daughter" nuclide.

Nuclei can also decay by capturing one of the electrons that surround the nucleus. Electron capture leads to a decrease of one in the charge on the nucleus. The energy given off in this reaction is carried by an x-ray photon, which is represented by the symbol hv, where h is Planck's constant and v is the frequency of the x-ray. The product of this reaction can be predicted, once again, by assuming that mass and charge are conserved.

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Any activity that produces or uses radioactive materials generates radioactive waste. Mining, nuclear power generation, and various processes in industry, defense, medicine, and scientific research produce byproducts that include radioactive waste

Radioactive waste can be in gas, liquid or solid form, and its level of radioactivity can vary. The waste can remain radioactive for a few hours or several months or even hundreds of thousands of years.

The primary obstacle in disposing of nuclear waste and cleaning nuclear development facilities is the duration of halflives of the elements that compose nuclear waste.

For example, Uranium 235 has a half-life of 703,800,000 years. The half-life is the number of years required for any amount of uranium 235 to decompose by half (Probst 1998).  Typically these elements will remain hazardous for ten times their half lives;