Answer to Question 1
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).
Answer to Question 2
Yes. The nuclei that are radioactive are so because their inner structures are less
stable than it would be without the extra neutron (beta-minus decay), proton (beta-plus
decay), or helium nucleus (alpha decay).
The resulting structures may be less stable against one or several of these changes also. If
so, that nucleus will be radioactive as well. There are many examples of this. The uranium
decay sequence by alpha and beta emission, which ends finally in lead, is one such example.
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Problem
Identification of the numbers in the Word Problem