One problem for civilian nuclear energy is the creation of long-lived radioactive wastes. Explain ...

The fuel of the reactor is uranium-235, which fissions. Because high-Z nuclei
have more neutrons per proton than low-Z nuclei, the fission products are normally neutron
rich compared to normal versions of the atom. Because of this, they are generally more
unstable, and radioactive decay is a process that leads to increased stability. Many will be
radioactive.
They are a problem because they can be dangerous from their thermal output as well as
from their radioactivity. They can be reprocessed to obtain useful isotopes, or the wastes can
be sequestered (the usual choice). The Yucca Mountain facility is to be the official
repository for civilian nuclear wastes (such as those from power plants).