A chemical element is defined by its atomic number, which is the number of protons in its nucleus. However, the atomic number does not specify all of the properties of a given atom, as the nucleus can also contain neutrons that do not contribute (much) to the chemical properties of the atom. These variations due to differences in neutron number are called isotopes. An isotope of an element is usually identified by its mass number, the total number of particles in its nucleus. For example, carbon-14 has eight neutrons in addition to carbon's six protons.
When most people hear the word 'isotope', they think of radioactive isotopes of common elements, often used in medicine as diagnostic tracers or sources for radiation therapy. As the conditions on the stability of an isotope are quite stringent, these radioisotopes vastly outnumber non-radioactive isotopes as an overall fraction of the number of isotopes. As 'normal' matter is mostly non-radioactive, though, radioisotopes are rare in common experience and have thus developed a strong association with the word 'isotope'.
Elements can have multiple stable isotopes. The most famous cases of this are two elements at opposite ends of the periodic table: hydrogen and uranium. The stable isotopes of hydrogen are protium, whose nucleus consists of a bare proton, and deuterium, which contains both a proton and a neutron. Deuterium is important as it undergoes nuclear fusion much more readily than protium, making high-yield, sustained fusion reactions possible. The relative difference in mass between protium and deuterium is larger than that between any two other stable isotopes, which alters the properties of deuterium compounds more than any other equivalent substitution. Heavy water is water containing deuterium rather than protium, which has a significantly different melting point, viscosity, and density than normal water.
Uranium does not, strictly speaking, have a stable isotope, being too heavy for complete stability. However, a number of its isotopes have multi-billion-year lifetimes and are effectively stable. The most common uranium isotope is uranium-238, but it is incapable of self-sustaining nuclear fission as the neutrons released by fission do not cause other U-238 nuclei to fission. On the other hand, uranium-235 quite readily undergoes fission when struck by a neutron, and so it can be used to create self-sustaining fission reactions in both nuclear reactors and nuclear weapons. Thus, the most tightly-controlled material in the world is uranium 'enriched' with a greater fraction of uranium-235.
Specific isotopes can be produced by a variety of methods. Light isotopes with relatively large mass differences can have reasonable differences in chemical reaction rates, with deuterium undergoing electrolysis from water slower than protium. Large-scale electrolysis plants are thus used to produce heavy water. The two uranium isotopes are very difficult to separate chemically and uranium is usually enriched in centrifuges which collect more of the heavy U-238 at the outside. Short-lived radioisotopes cannot be enriched from natural materials and must be artificially produced. Commonly, a sample is bombarded with high-energy protons, some of which are captured by the nuclei in the sample to produce new isotopes.
Different isotopes are, of course, important in nuclear physics, where often the concepts of element and isotope are combined to describe 'nuclides'. Large-scale radioisotope beam facilities such as ISOLDE at CERN and ISAC at TRIUMF are invaluable tools for probing the structure and interactions of nuclei, with consequences for astrophysics, particle physics, and atomic physics, among other fields.
This writeup is copyright 2008 D.G. Roberge and is released under the Creative Commons Attribution-NonCommercial-ShareAlike licence. Details can be found at http://creativecommons.org/licenses/by-nc-sa/3.0/ .