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[Though initially the question may seem to belong to stack exchange chemistry but I believe that I would get a better physical explanation over here. ]

Currently I was reading about electron affinity of elements and found that for most of the release energy when an electron is added to them , this made me question why this is so? So I searched and found an answer on chemistry SE. But in the answer it states

When a system goes from a higher energy state to a lower energy state, it loses energy.

But considering the electron and nucleus as a system shouldn't the energy remain constant if the net external forces acting on the system is zero.But if I'm going wrong somewhere can you explain why and where I'm going wrong? Also please explain if you know as to what is really happening and why the energy is released.

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When an electron is bounded by the electric charge of a nucleus, it doesn't have enough energy to "run away" to infinity. Meaning you actually need to give energy to the electron to tear it apart from the atom, creating an ion (that is the meaning of ionizing energy).

Looking at it the other way around, if you have a free electron and you want it to bind to an ion to form an atom, you need to take energy from it. Of course, the total energy of the system should be conserved, so some of that energy is released as kinetic energy of the whole atom (meaning some energy goes to the nucleus) but some energy also goes to light. This is quite a general thing to consider: when a charged particle loses energy, because it is always coupled to the electromagnetic field, it can always transfer energy to the field itself (of course only if the conservation laws hold).

This effect is actually what makes florescent light bulbs/ Mercury lamps/ Sodium lamps (etc..) work. You create an electric voltage so high it ionizes the atoms of gas inside the lamps (the electric energy gives energy to the electrons to "run away" from the atom - sometimes not enough to really ionize but enough for the electron to go to a higher energy state of the atom). Then, electrons recombine with the ions, giving away some of that energy as light with specific wavelengths, depending on the energy state they began and finished.

I hope this explanation helped, you are welcome to ask more questions about it.

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This Because of the Decrease Potential Energy (of the attractive force) between the Nucleus and the electron (Which Dominates over the the increase in potential due to electron -electron interaction)

You can think of it as the electron "Falling down" the "Potential well" and thus releasing energy (like a ball which falls down hits the ground releasing energy)

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