To make my question clear, i'll talk about the hydrogen atom. The energy of the electron level is -13.6 eV / n^2. This means that the higher the orbit (n), the higher the energy. Still, i've always read that K-shell (n=1) electrons are strongest bound. Yet when an electron goes from a high level to a lower one, a photon is released. Maybe the minus sign confuses me? But an electron with n=5, as rare is it may be, would have an energy of -0.5 eV, while one in the ground state has -13.6 eV. So, you'd think the n=1 state is more tightly bound, but if that is the case, then it would seem logic for an electron to REQUIRE energy (say, a photon) to go down to lower n-state, but instead, it releases energy. How does it work?