Energy level diagrams are a means of analyzing the energies electrons can accept and release as they transition from one accepted orbital to another. These energies differences correspond to the wavelengths of light in the discreet spectral lines emitted by an atom as it goes through de-excitation or by the wavelengths absorbed in an absorption spectrum. Using the Bohr Model, the energy levels (in electron volts, eV) are calculated with the formula:
E_{n} = -13.6 (Z^{2}/n^{2}) eV
where Z is the atomic number and n is the energy level. The ground state is represented by n = 1, first excited state by n = 2, second excited state by n = 3, etc.
Using Bohr's formula, a hypothetical, doubly-ionized atom with Z = 3 could have the following energy level diagram. Notice how each energy level closer and closer to the nucleus is more and more negative. This signifies that the electron is trapped in an "energy well." To ionize a ground-state electron [to take it from -122.4 eV to 0 eV in our example], you would have to irradiate the gas with photons having energies of 122.4 eV or greater. This is the ONLY instance where the incident energy does not have to EXACTLY match the difference in two energy levels. Any excess energy would remain in the form of the ionized electron's kinetic energy. Max Planck had already determined that the energy levels in an oscillating system were quantized and followed the relationship E = hf where f represented the frequency of oscillation and h is Planck's constant, 6.63 x 10^{-34} J sec. In our case, f is the frequency of the emitted photon in accordance with c = fλ. If we replace f with c/λ, we have the formula
E = h(c/λ) The value of E, or energy, represents the difference in the energies of two energy levels (ΔE) when an electron goes through de-excitation. The value of λ corresponds to the wavelength of the emitted spectral line. λ = hc/ΔE |