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The liquid-drop model is able to reproduce many features of nuclei, including the general trend of binding energy with respect to mass number, as well as the phenomenon of nuclear fission.
Nuclei with certain numbers of neutrons and protons (the magic numbers 2, 8, 20, 50, 82, 126,...) are particularly stable, because their shells are filled.
Nuclei may also have extreme shapes (similar to that of american footballs) or extreme neutron-to-proton ratios.