We have seen what happens when an electron gains energy from its ground state. The electron goes to its excited state, then falls back down emitting a photon. This has been when we have given small amounts of energy to the electron. Something else happens if we give a large amount of energy to an electron.
We set our equation to give us no y-intercept by setting E=0 at n=infinity. The energies of the levels are negative, which shows that WE are supplying energy to the electron to move it to its excited state. The energy of an electron's ground state shows the amount of energy needed for the electron to escape the atom. We need to keep E=0 at n=infinity, because if we moved the electron to an infinitly high energy level, the electron should be able to become free. With a y-intercept, that would mean we still had to supply more energy to the electron for it to become unbound from the atom, but no energy levels would be available. In other words, this is not seen experimentally. Free electrons are said to be ionized. The energy it takes to remove an electron from its ground state is called ionization energy. The Hydrogen Spectra showed specific amounts of energy at low numbers of n (1, 2, 3, etc.). As the n increases the energies seen look almost continuous.
With the Hydrogen atom, set at E=0 at n=infinity, what energy is the lowest energy state (n = 1)? What would happen to the electron if we gave it 15eV? What would happen if we gave an electron enough energy to reach E=0?
With 0 eV energy, the electron loses its interaction with the atom. When an electron is not bound by the atom, we say that the atom has become ionized. The energy required to take the electron to E=0 is called the ionization energy.