According to Bohr, electrons orbit in circular orbits at fixed distances around the nucleus. Since the kinetic energies required to stay in these orbits are constant, the differences in energies between these orbits are constant. When an electron is excited (moves to a shell that it does not occupy in the ground state), it eventually falls back down to fill the hole. When this happens, the energy difference is released as light (A particle of light is a photon, its energy is determined by analyzing it like a wave, so the energy of the photon E = hf.) This pattern of photons is what is released when an atom (Hydrogen, in the examples above) is excited then allowed to relax. These are also the same energies which the atom can absorb while still keeping the electron in one of its energy shells.
If a photon of too great an energy hits that electron, then its kinetic energy will be too great to stay in orbit at all, and the atom will be ionized. This is the basis of the Photoelectric Effect, discovered by Einstein: A low-intensity (dim) beam of light of the right color can ionize some metals (like Magnesium), but even the brightest beam of light that is just too low-energy cannot. Some of the energy of photon is used to fight against the negative Work done by the Electrostatic Force as the negative electron moves away from the positive nucleus. The amount of energy that is pulled out of the electron is called the “Work function” (Φ) of the electron.
Bohr’s theory works well for talking about the transitions between different energy shells, but it is incomplete. The 4 quantum numbers (n: shell, l: subshell, ml: orbital, and ms: spin) make up a complete “address” for each electron within an atom.
The biggest difference between the Bohr and quantum models occurs in the way they describe the movement of the electrons. Electrons are now quantum objects, whose location cannot be determined with perfect accuracy. Thus, we talk about the “electron cloud” that is a probability distribution of where the electron is. When the electron gets excited to a new energy shell, that cloud becomes a spherical shell of greater radius.
Each subshell holds orbitals, regions of space that can hold up to 2 electrons. The azimuthal (orbital) quantum number mℓ ϵ [-ℓ,ℓ ]. This means that in each subshell, the number of possible orbitals is an odd number (Since when ℓ =0, mℓ can only have one value, 0, so the s subshell can only have one orbital). The orbitals in a given subshell are arbitrarily assigned subscripts to describe them. However, they all contain the same volume, so they all are equivalent in the energy an electron must have to occupy them. s orbitals are bigger than a single p orbital, so the electrons there are more relaxed. When the orbitals hybridized, they have to average the volume for each electron. Thus, in energy terms, s < sp < sp2 < sp3 < p.
The final quantum number is ms, or spin. Think of two roommates who hate one another, and imagine they share a 2-bedroom with a common area. The only way they can both use the common area is if one becomes diurnal and the other nocturnal. This is the only way they can be in the same place at the same time. This is analogous to the repulsion electrons feel. Only by having different spins can they be in the same orbital. ms ϵ [-½, +½].
Hund’s Rule tells us how electrons are arrayed in the ground state of an atom. If each subshell is a city bus with seats arranged in pairs, every electron choosing a pair of seats (orbitals) in which the other one is empty first. Before a whole new bus is called into service, though, the electrons will double-fill seat pairs (orbitals) until all the orbitals in a shell are full.
This does not apply strictly to transition metals, because the energy difference between, for example, the 4s and 3d subshells is so minimal that atom can transition electrons between those subshells to satisfy Hund’s Rule.
The graph at right shows the energies of the different subshells (each square is an orbital). Thus, the ground state configuration for Chromium (Z=24) is [Ar] 4s13d5, which maximizes the number of fully-filled and half-filled subshells for that atom.