Why the total energy of an electeon is negative?
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Ar first I was thrown off by the claim that the total energy of an electron is zero. That just doesn't happen. The negative energy you are writing about is of the system of electron plus nucleus and any other electrons that happen to be in the atom. It is the energy of the atomic system.
Individual electrons are singled out because their kinetic energies change more than the kinetic energy of the rest of the atom in going from one orbital to another or in being knocked out of an atom.
However, the very important potential energy is not in the electron. It is stored in the electric field between electron and the rest of the atom. This is the energy term that is negative, and when an electron is bound to an atom this negative energy plus the positive kinetic energy still totals negative.
However, the potential energy of the system is only negative if we choose to say that the zero point for potential energy of the system is for a large separation between the electron and the rest of the atom. Choices of zero points for potential energies are physically arbitrary.
The choice of zero potential energy as that for an infinite separation simplifies both the math and the energy explanation for when an electron is bound to an atom.
If we imagine taking the electron farther and farther from the atom, the potential energy would become less negative and approach zero at infinite separation. If it is necessary to add positive energy to the system of electron plus the rest of the atom to free the electron, the electron must have been bound to the atom previously.
The negative total energy of the system is just a quantitative indication that to completely remove the electron, energy must be added.
Individual electrons are singled out because their kinetic energies change more than the kinetic energy of the rest of the atom in going from one orbital to another or in being knocked out of an atom.
However, the very important potential energy is not in the electron. It is stored in the electric field between electron and the rest of the atom. This is the energy term that is negative, and when an electron is bound to an atom this negative energy plus the positive kinetic energy still totals negative.
However, the potential energy of the system is only negative if we choose to say that the zero point for potential energy of the system is for a large separation between the electron and the rest of the atom. Choices of zero points for potential energies are physically arbitrary.
The choice of zero potential energy as that for an infinite separation simplifies both the math and the energy explanation for when an electron is bound to an atom.
If we imagine taking the electron farther and farther from the atom, the potential energy would become less negative and approach zero at infinite separation. If it is necessary to add positive energy to the system of electron plus the rest of the atom to free the electron, the electron must have been bound to the atom previously.
The negative total energy of the system is just a quantitative indication that to completely remove the electron, energy must be added.
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