We have to be very careful here !
An electron that has any energy can go galavanting around on its own, sight-seeing and doing its own thing. That's not the situation with the electrons in an atom. The energy of every electron in an atom is negative ... it "owes" the atom energy, and that's why it stays bound to it. You have to pull on the electron ... give it some more energy ... in order to break it free from the atom.
The electrons that are way out in the outer orbits are the easiest to rip away from the atom ... they don't "owe" the atom much, their energy is the least negative, and you don't have to give them much to settle their debt and release them from the atom.
The electrons that are down deep, closest to the nucleus, are the most tightly bound. They're the ones whose energy is the most negative, and it takes a team of horses to pull them free of the atom.
I know I'm going to catch flak for this answer, but I do believe it's the most technically correct one: The electrons with the least energy are the ones whose energy is most negative ... those in the first orbital, down deep in the atom, close to the nucleus.
Electrons with the least energy in an atom are found closest to the nucleus, specifically in the innermost orbital. These electrons are more negatively charged and more tightly bound, making them more stable. In contrast, electrons in outer shells have higher energy and are less tightly bound to the nucleus.
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