What is the reason why atoms contain the same number of electrons and protons?

An electron is a negatively-charged particle, while a proton can be described as a positively-charged particle. Because the negative charge attracts the positively charged, and vice versa. Both electrons and protons stay together, so their overall charge is neutral. To remain neutral, an atom must always have equal electrons and prototons.

Nature tends to maintain equilibrium. A stone that is lying on the ground, for example, is in equilibrium. If the stone is lifted, it loses equilibrium and has the potential to fall towards ground. An electron can also be considered a particle with a negative potential, but not in equilibrium. The positive potential proton will only bring it near enough to make it reach its equilibrium (or neutral) state. Therefore, electron and proton are always in a pair.

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