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The nucleus of an atom is held together by the strong force, to which both protons and neutrons contribute. The problem is that protons also contribute to the electromagnetic force, which repulses the protons from each other. The strong force has a much smaller range than the electromagnetic force, so in large atoms, protons only receive the attractive strong force from the protons around it while receiving the repulsive electromagnetic force from all of the protons in the nucleus. This is why large atoms tend to be unstable, and where neutrons come in. Neutrons add to the attractive strong force while having no charge that would add to the repulsive electromagnetic force. Without neutrons, the larger atoms could not stay together, their nuclei would be destroyed.

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Q: Why do you think that atoms have neutrons?
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