This came up when I was studying about atomic structure, specifically the Bohr model. There, the explanation I was given for the total energy being negative was – the energy of a free electron at rest is zero. Then, an electron in a atom will have less energy than the free electron due to virtue of being stabler. Hence, the energy is negative. So, why are electrons in an atom stabler?
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An electron is attracted to the protons of the nucleus. This pulls it downward – closer to the nucleus is a lower-energy state.
Our choice to label the energy at infinity zero is mainly a matter of convention, although it is a convention that makes sense because it is the least arbitrary point of reference.
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