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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A free electron is stable.
If the electron is bound in an atom then you have less overall energy than with a positively charged ion and a free electron far away because the electron and the ion attract each other.
It’s similar to gravity where energy is released if you drop something (make it get closer to Earth, which attracts the object).
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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