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Protons and electrons are held together in the atom through the electrostatic force of attraction.

However, the electrostatic works between any particles, so it should affect protons and protons by making them repel each other and therefore blowing the nucleus of an atom apart. This does not happen because there is a second force at work; the strong nuclear force which (at separations larger than 0.5 femtometres to 3- 4 femtometres) is a attractive force which overcomes the electrostatic force of repulsion and therefore stop the atom being blown apart!

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