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.
