## A Metaphor for the Concept of Orbitals

In order to give you some idea of what an orbital is and what information it provides we will use an analogy of an atom as an apartment house.  The rooms in the house of the atom are the homes of the electrons.  Each room has different characteristics--different energies and different locations in space are the two with which we will be most concerned.  We can picture the house shown below, a rather unstable, precarious

structure, which has one room on the first floor, four rooms on the second floor,  nine rooms on the third floor, and so on.  Two electrons can live in each room as long as they are compatible--they must have opposite spins.  The electrons on the second floor have a higher energy than those on the first floor (after all they have to go up one flight of stairs to get to their rooms).  Three of the rooms on the second floor actually have a higher energy than the other room.  We might imagine for the sake of our metaphor that there is a three step flight of stairs going up to the three rooms on the second floor.  The electrons in these three rooms are called p electrons, while the two in the other second floor room are called s electrons.  Moreover, in the quantum mechanical world of the atomic scale, electrons are not confined to their rooms (how lucky they are) and their positions are only known as probabilities.  For example, an electron "living" in the s room on the second floor is known to exist within a sphere surrounding its room and is most likely to be in its room, but if you open the door of the second floor s room (let’s call it the 2s room) at any particular time, you may or may not find the electron in the room.  The electrons in the 2p rooms not only have a slightly higher energy than the 2s electrons but they also must travel in different circles (pun intended).  Their locations are more restricted to one of the three x, y, or z-directions from their rooms.  The electrons in one of the 2p rooms can be found mostly along the x-axis, for example (these are referred to as the 2px electrons).

When we want to keep a record of the electrons in the house we write out the electron configuration.  For sodium it is 1s22s2p63s1.  This inventory of the energies and location probabilities of the electrons in an atom is taken when the atom is in its ground state; that is, when the electrons are not excited.  The inventory for the sodium atom could be read as: Two electrons are in the lowest energy orbital with a high probability of being distributed evenly within a sphere; two electrons also have the spherical electron distribution but have a higher energy than the 1s electrons; six electron (two in each of three orbitals) have a slightly higher energy than the 2s electrons and have their greatest probability directed along one of the three Cartesian coordinates; and one electron has a spherically symmetric probability distribution with a higher energy than the 2s electrons.  For convenience we list all of the electrons in the p-rooms or orbitals together.

When the sodium atom loses an electron, it loses the one with the most energy, which is the one on the third floor.  That gives the resulting sodium ion the electron configuration of 1s22s2p6.

Every apartment has a landlord.  In our metaphor the landlord lives in the basement of the inverted A-frame.  The atomic level landlord is the nucleus--all of the protons and neutrons that are present in the nucleus of the atom.  The nucleus, like a real landlord, is aggressive and maintains control of the inhabitants of the apartment.  In the case of atoms the positive charge of the nucleus exerts a large force or attraction on the negatively charged electrons (remember that opposite charges are attracted to one another).  The extent to which the atom is "eager" to accept or release electrons depends mainly on the attraction of electrons to the nuclear charge (and to a lesser extent on the shielding of the nuclear charge produced by the other electrons) and on the stability of the atom after the electron has been accepted or released.  Although it may seem that every orbital should experience the positive charge of the nucleus to the same extent; that is not the case.

Let's return to our apartment house analogy to see why electrons in different orbitals experience the positive charge differently.  Suppose that the landlord, the nucleus, has a positive charge of plus seven. Because an electron on the first floor in the 1s orbital is closer to the nucleus than an electron on the 3rd floor in a 3s orbital, the 1s electron is more strongly attracted to the nucleus.   Generally, the energy of the electron in a given orbital is strongly influenced by the attraction to the nucleus as well as repulsions by other electrons in other rooms (those darn neighbors are frequently cussing up a storm while playing those computer games!).

Of course, our analogy breaks down in a number of other ways, but for now it  gives us an idea of what an orbital is—it is a room in the house of the atom and this room defines the energy and the probable location of two electrons.   The probability aspect of this metaphor is very important: in the atomic world there is no certainty, everything is a matter of probability.  This probabilistic nature is expressed by the Heisenberg Uncertainty Principle: For two properties of a particle such as position and energy, the more precisely one of these properties is known, the less precisely the other can be known.  In other words, if we know the energy of a particle very precisely, the location of the particle cannot be known very precisely.  These uncertainties can be expressed as standard deviations (s) and the following equation holds, where h is Planck’s constant:

s(energy)s(location) ≥ h/2π