What is the most important piece of knowledge that practitioners of nuclear physics wish to convey to the general public?
Many unsuspecting citizens have been led astray by the example of certain prominent public office holders who insist on pronouncing the word "nuclear" as nuc-u-lar. Nuclear physicists invariably frown on this practice, and strongly endorse the nu-clear pronunciation. If you care to delve further into the world of nuclear research, we suggest that you browse Michelle's selection of educational cartoons about nuclear physics. (A couple more such cartoons can be found).
For a more intellectually challenging primer on nuclear physics, we recommend starting from An Interactive Tour of the Inner Workings of the Atom, courtesy of Lawrence Berkeley National Lab.