general chemistry - why is energy released when an electron is added to an atom?

[Monkeymaniac]

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Ok, so I understand that electron affinity values of many elements are negative, meaning that energy is released when a new electron is added to the atoms, and that the affinity value depends on the attraction force between the added electron and a postiive nucleus.

But how does this attractive force decrease the energy of an atom? No books/references seem to go this deep and explain about it. Does anyone have any idea?

 

[Isoprop]

Think of the Bohr atom. Energy is required to excite an electron from n = 1 to n = infinity. Why? Because of electrostatic forces between the positively charged nucleus and negatively charged electron.

Conversely, an electron that is added from infinity to its ground state goes from a high energy state to a low energy state. That energy is released.

Edit:

But how does this attractive force decrease the energy of an atom?

To expand, the attraction between the nucleus and the electron means that the closer they are, the lower their states of energy. So the electron is going from a high state of energy to a low state of energy. It's like gravitational potential energy. You are attracted to the Earth by gravity so you are at a lower state of energy on the ground then you are at the top of a skyscraper.