Eric Schiff, chair of the department of physics at Syracuse University, provides this explanation.
Image: Courtesy E. SCHIFF/Syracuse University
It's much easier to explain why neon isn't inert in a discharge tube than it is to explain why it is inert to chemical reactions. The voltage across a discharge tube will accelerate a free electron up to some maximum kinetic energy. The voltage must be large enough so that this energy is more than that required to "ionize" the atom. An ionized atom has had an electron plucked out of an orbital to make it a "free" particle, and the atom it leaves behind has become a positively charged ion. The resulting plasma of charged ions and electrons carries the electric current between the tube's electrodes.
The photo (above) shows a gas discharge sign designed by Sam Sampere of Syracuse University. This sign incorporates a neon discharge tube (the orange word "Physics") and mercury discharge tubes (the blue word "Experience" and the outer frame). The sculpture at the bottom of the sign represents the electric and magnetic fields of light. The white and yellow sine waves in the sculpture are actually fluorescent lights. These fluorescent lights are mercury discharge tubes with special coatings on their inner walls. The ultraviolet light emitted by the mercury discharge inside a tube is absorbed by the coating, which subsequently emits light of a different color (and with a lower photon energy). Depending on the exact material of the coating, a whole range of colors can be obtained.
So why do these gas discharges emit light? As an alternative to being removed by an energetic collision, an electron on an atom can be excited. One speaks of the electron as having been promoted to an orbital of higher energy. When the electron eases back down to its original orbital, a particle of light (a photon) carries away the energy of excitation¿and the discharge tube glows! A photon's energy (its wavelength or color) depends on the energy difference between orbitals. A given atom can emit photons at many energies corresponding to its different pairs of orbitals. This series of photon energies¿the emission lines to a spectroscopist¿is unique to a particular atom. As can be seen in the sign, the mercury discharge tubes have a very different hue than the neon discharge tube does. The inert gas helium was actually discovered this way, and observations of sunlight revealed a series of photon energies that had never before been seen in discharges on the earth.
The chemical inertness of certain gases is subtler to explain. Generally speaking, when two atoms come into proximity, the highest energy, or valence, orbitals of the atoms change substantially and the electrons on the two atoms reorganize. If this reorganization lowers the total energy of the electrons involved, a chemical bond can form. For ordinary, non-inert atoms, the electrons are relatively pliable and bonds often form. The electrons in inert gases, however, are relatively resistant to this proximity effect, so these gases very rarely bond to form molecules.