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Neutrons and atoms
Neutrons are found in the nuclei of all atoms that are heavier than hydrogen. The chemical behavior of an element is determined by the electronic structure bound to the nucleus, and it is the number of protons in the nucleus that determine the nuclear charge which is balanced, for the atom, by the number of electrons. However, the mass of the nucleus varies with the number of neutrons, differing numbers of neutrons defining different isotopes.
Except for hydrogen-1 (a bare proton) and helium-3 (two protons and one neutron), isotopes of elements with fewer neutrons than protons are not stable (i.e., they emit radiation as they decay into other elements). Stable heavier elements have either the same number of neutrons as protons or have more neutrons.
The heaviest fully stable element is lead, with 82 protons, and three stable isotopes with 124 to 126 neutrons.
Neutrons that are not part of a nucleus are, themselves, unstable. They have a half-life of about 15 minutes, and decay into a proton, an electron, and an electron antineutrino.
Because a neutron has no electric charge, it can nuzzle up nice and close to a (positively charged) atomic nucleus without being repelled. If conditions are right, this nucleus can capture the neutron, adding it to its contents. This results in the nucleus becoming a new isotope of the same element; a carbon-12 nucleus that captures a neutron, for example, would become a carbon-13 nucleus. Depending on the nucleus that did the capturing, the new resulting isotope can be radioactive. If a non-radioactive cobalt-59 nucleus captures a neutron, for example, it becomes radioactive cobalt-60. Nuclear scientists refer to this process as "neutron activation", but most folks call it radioactive contamination.
Nuclear fission results in neutron radiation, consisting of free neutrons. This radiation can be blocked by water, concrete, and paraffin wax.
The speed of emitted neutrons makes a difference as to how often they get captured by the nuclei they run into. Fast neutrons are rarely captured, but the slower thermal neutrons are much more likely to be captured.