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Protons and neutrons exit together in an...

Protons and neutrons exit together in an extermely small space within the nucleus. How is this possible when protons replel each other?

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Nuclei are stable because of the presence of anothere, short - range (about 2fm) froce, the nuclear force. This is an attractive force that acts between all partilces. The protons attract each other via the nuclear force, and at the same time they repel each other through the Coulomb froce. The attractive nuclear force also acts between pairs of neutrons and between neutrons and protons. The number attractive forece is stronger than the Coulomb repulsive force within the nucleus (at short ranges). If this were not the case. stable nuclei would not exist.
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