1. Atomic theory and atomic structure
   1. Evidence for the atomic theory
   2. Atomic masses; determination by chemical and physical means
   3. Atomic number and mass number; isotopes
   4. Electron energy levels: atomic spectra, quantum numbers, atomic orbitals
   5. Periodic relationships including, for example, atomic radii, ionization energies, electron affinities, oxidation states

In this article, I review the principal components involving electronic structure but not nuclear structure.

In college courses designed for students who have demonstrated success in first-year high school chemistry (for example, on the SAT® Subject Test in Chemistry) and/or attempted AP Chemistry but did not earn a high exam grade, the first topic covered is often atomic structure.

Background
Students should receive a modest historical introduction reviewing the ideas and experiments of Dalton, J. J. Thomson and Rutherford, and Bohr that established the bases of atomic theory and structure as matter consisting of atoms, each with a central positive nucleus surrounded by negatively charged electrons. Students must firmly master this notion before proceeding.

It is also essential that students have a firm grasp of the properties of electromagnetic radiation, since the results of its interaction with atoms is crucial to understanding the experimental evidence that led to the development of the modern picture of atomic structure. Students should have fully mastered the relationships between wavelength, frequency, and energy, and they should know, for example, the relative energy and frequency ranges of ultraviolet vs. visible vs. infrared radiation.

Energy in Electronic States of Hydrogen Atoms — The Bohr Model
It is helpful if students can view a hydrogen discharge lamp through a diffraction grating to see for themselves the evidence of transitions between electronic energy states that led Bohr to propose his model of the electronic structure of the atom. They must understand that the energy (and hence frequency and wavelength) of emitted light corresponds to the difference between the initial higher-energy state of the electron and the final lower-energy state into which the electron moves. Make sure students identify that they are considering a hydrogen atom, so only a single electron is present in the atom and no other electrons need to be considered (e.g., there is no screening of the nuclear charge).

Confusion exists in many students' minds regarding the meaning of "higher" and "lower" with respect to position and energy states. For all energy diagrams in chemistry, higher energy corresponds to less stable situations. For understanding this, analogies to gravitational potential energy may be useful. It takes energy to push a rock to the top of a hill. As a rock rolls downhill, it loses gravitational potential energy. For the hydrogen atom, lower energy corresponds to a more stable position with the electron nearer the nucleus. (Since the Coulomb force between the electron and nucleus is attractive, it takes energy to pull the electron away from the nucleus and doing so puts the atom into a less stable configuration.) Confusion may arise relating to the convention used for the zero of energy. In the hydrogen atom, the convention is to define the zero of energy as zero interaction between the electron and nucleus (i.e., infinite separation). For chemical bonds, the zero of energy is occasionally placed at the bottom of the potential energy surface (i.e., the equilibrium bond length). Independent of where the zero of energy is placed, higher energy corresponds to less stable situations. Also, the differences in energy are independent of the choice of the zero of energy.

Thus we may read that an electron with a higher-energy state (say n = 5) "falls" into an n = 2 state and releases blue light as it does so. The n = 2 electron is closer to the nucleus, in a more strongly attracted and hence lower-energy condition than the n = 5 electron. The change in energy has been converted into electromagnetic energy, and the atom is now in a more stable condition. Since we define the hydrogen atom's potential energy as zero when the electron is at an infinite distance away from the nucleus, the potential energy becomes increasingly negative as the electron moves closer and closer to the nucleus. So, in energy diagrams, zero is at the "top," and energies become less negative, not more positive, as one moves "up" on the diagram. Students will need careful guidance to pay attention to the sign of the energy and realize that, for instance, -100 kJ/mol lies above -200 kJ/mol.

An exam question may ask students to compute electromagnetic radiation energies (E_emr) from changes in positions in hydrogen atoms. The exam booklet provides a version of the Bohr equation containing the appropriate Rydberg constant (E_n = -2.178 x 10^-18/n² joule). ΔE_atom = E_{final state} - E_{initial state} gives the electromagnetic radiation energy released or absorbed by the system. For an n = 5 to n = 2 transition, this equation generates a negative value for ΔE_atom, correctly indicating that the atom system has transferred energy to its surroundings (exoergic process). For the n = 2 to n = 5 transition, ΔE_atom is positive, indicating the atom has absorbed electromagnetic energy.

Hydrogen atom spectral lines involving absorption of electromagnetic radiation are observed in the sun's spectrum as the cooler outer layers of hydrogen in the sun absorb electromagnetic radiation emitted from the hotter inner core. Establishing the underlying principles of these transitions firmly in students' minds will serve them well in future chemistry studies. They will see many more examples of emission and absorption spectroscopy and spectrometry in all the wavelength regions of electromagnetic radiation, from gamma radiation to radio waves.

Beyond the Bohr Model
The Bohr model was extremely successful in modeling observations with hydrogen atoms. However, it failed to meet the same challenge for all other atoms. Attempts to "tweak" the model were not too successful until Schrödinger, de Broglie, and Heisenberg contributed (in different ways) to a greater understanding of the behavior of electrons in atoms. The net result is the quantum picture we now use, where electrons still have discrete energies associated with their atomic positions but occupy positions called orbitals, the shapes of which we can generate with computer modeling but will probably never observe. You can find calculated "shapes" of orbitals in texts and on several Web sites. It is unfortunate that the term "orbital" bears a close similarity to "orbit," coined for the defined pathway of objects rotating around other objects, since beginning students still tend to think of orbitals as resembling orbits.

If possible, encourage your students to think of orbitals as "something completely different" (with apologies to Monty Python). Electrons in atoms (not necessarily in outer space) take on predictable but unusual shapes, best identified as "probability distributions" that retain highly specific potential energy states, known because transitions between such states still result in electromagnetic radiation line spectra. However, we cannot predict the energies from simple formulas when more than a single electron is present because of the interactions between the electrons as well as between the electrons and the nucleus. We still need complex approximations (except in the very simplest cases) to get the "right" answers from computer models.

This much has evolved from the original Schrödinger model: each electron's energy equation is characterized by a set of four integers called quantum numbers. Rules (clearly described in textbooks) establish the allowed ranges of these numbers. No two electrons in any atom can have the same values for all four numbers. The rules, combined with a well-established filling order (aufbau principle) determine the structure of neutral ground-state atoms, as well as the possible excited states where electrons can occupy previously unoccupied orbitals.

Many students appear to master these rules quite well, though they may need continual reminders that the rules specify the structure of a neutral ground-state atom.

When writing electron configuration listings for an atom, we use symbols that represent particular sets of quantum numbers. These symbols evolved, unfortunately, from empirical work by spectroscopists carried out before Schrödinger's work established a more workable model. The basic shape of the orbital derives mostly from the value of the angular momentum quantum number ( ). Thus we identify the simplest electron group (or subshell) with   = 0 by its overall spherical shape, and we refer to it with the symbol s (for single). If  = 1, the symbol is p (for principal); when   = 2, the symbol is d (diffuse); and for  = 3, the symbol is f (fundamental). When  = 4, used only in the actinide elements discovered much later, the symbol is g (the letter after f), which at least makes some sense. Tests included with textbooks and former AP Exams give many examples of how to use these symbols, the aufbau principle, and other quantum number rules in writing electron configurations for atoms.

The most common error that students make is the easily avoidable one of not counting the correct number of electrons (equal to the atomic number for a neutral atom). They also fail to take into account the loss or gain of electrons if the subject species is an ion.

How Atomic Structure Affects Atomic Properties
The chemical behavior of an atom is entirely determined by its electronic structure. Chemistry is a discipline often described as "the study of electrons in atoms." To learn how atomic properties change in a systematic way, the easiest way is to understand and master the relationship between the electronic structure of an atom and its location in the periodic table. Initially, scientists used the periodic table as a way to systematize the observed chemical behavior of the known elements. Now we also understand it as an organized record of the electronic structure of the atoms of those elements.

[Side note: Beginning students may have difficulty distinguishing the term "atom" from the term "element." Indeed, scientists often seem to use the terms interchangeably. We consider many elements to be atoms, but several behave quite differently from their isolated atoms. In fact an isolated atom (free from any interaction with its surroundings) may exhibit entirely different properties than when it is an "elemental state," a condition that usually implies some mole quantity of atoms, organized in some way as cluster, molecules, or network solids.]

The AP Exam often asks students to explain the periodic variation (or "trends") of properties such as atomic radius, ionization energy, electron affinity, and electronegativity. Students must also compare two specific atoms in terms of such properties. At the AP level, it is vital for students to understand that their "explanations" must demonstrate their understanding of how the underlying atomic structure influences the property, not just that it varies "from left to right" across a period, or "from top to bottom" in a family.

It is also vital that students begin with a proper understanding of the definition of the property they are explaining. Many students exhibit only a weak mastery of the definition of these properties, especially the sign conventions involved.

Some Clarifying Definitions
Ionization energy -- The energy change associated with removing one electron from a neutral ground-state (usually) atom: The electron is moved an infinite distance away. This energy is always a positive number since energy must be added to the atom system to remove an electron (always an endoergic process).

Electron affinity -- The energy change associated with adding one electron to a neutral (usually) ground-state atom: The electron comes from infinity. By proper sign convention, this would be a negative number if the result is energy transferred from the atom system to the surroundings (exoergic) and a positive number if energy from the surroundings is transferred to the atom (endoergic; energy is necessary to keep the electron on the atom). Some older texts may use the opposite sign convention, defining the electron affinity slightly differently.

Electronegativity -- Relative ability of an atom to attract electrons when bonding with another atom in a molecule: Scientists have tried different ways to compute such values. The most popular is that of Pauling, who compared the bond energy of a molecule Q-X with that of the average bond energy of Q-Q and X-X molecules. In some sense, this single parameter reflects the comparison of ionization energy and electron affinity as applied strictly to chemical bonding.

Atomic radius -- The value of the effective radius of a neutral ground-state atom as estimated by some form of measurement: The distance between atoms in various compounds is the covalent atomic radius. If the atoms do not readily form useful compounds, we must use other techniques. Metallic radius represents the distance between atoms in a solid metal. The most difficult to determine are the noble gases, for obvious reasons. The numbers are rarely as accurate (three significant figures!) as they are listed in some texts; they should be used only in comparing similar elements (as they will have been determined using the same method). We assume the values represent the approximate size of the electronic "cloud" and it is roughly spherical, surrounding the nucleus of the atom. Recent use of atomic force microscopy tends to confirm that these assumptions are reasonable.

A "deep" explanation goes right to the core of the atom. As one example:

Why is the first ionization energy of sodium (495 kJ/mol) different from that of potassium (419 kJ/mol)?

Point 1: The electronic configuration of a neutral ground-state sodium atom (Z = 11) is 1s²2s²2p⁶3s¹; potassium (Z = 19) is 1s²2s²2p⁶3s²3p⁶4s¹.

Point 2: The outermost electron is the one removed first as any atom is ionized.

Point 3: The first electron removed is 3s for sodium and 4s for potassium.

Point 4: The 3s electron in sodium is attracted by a nucleus with 11 protons; the 4s electron in potassium is attracted by a nucleus with 19 protons.

Point 5: We might first think that the potassium electron is harder to remove (more protons attracting it).

This is obviously not correct, so what else is changing?

Point 6: Atomic radius issue -- the 4s electron in potassium is further from the nucleus than the 3s electron in sodium (the data support this: the radius of Na is 186 nm, and the radius of K is 227 nm). The Coulomb force of attraction (and the energy resulting) is less as the distance increases between the charges.

Point 7: Shielding issue -- the presence of other electrons influences the property of each electron considered. Electrons are negatively charged, so the presence of inner shells of negative electrons tends to shield or "screen" the outermost electron from the effects of the nucleus. Strictly what the inner electrons do is lower the effective nuclear charge and thus the Coulomb force of attraction on the outer electron resulting from the nucleus. Students are allowed to state that the inner electrons "help to neutralize" the nuclear charge, as long as that doesn't imply that these electrons reduce the actual charge on the nucleus. It would be a bit like putting nasty-tasting JELL-O® between yourself and an attractive dessert. The attraction of the dessert seems much less if you have to fight through the JELL-O to get it.

Point 8: In summary, the combined issues in points (7) and (8) must overcome the effect discussed in point (5) so that the first ionization energy of K is significantly lower than that of Na. This explains the trend in the entire family of alkali metals in Group 1 of the periodic table.

Students do not need to use all of the above arguments for full credit on the AP Exam. However, a student who can think through all eight points will have truly mastered how to explain in terms of atomic structure, observed trends, and differences in atomic properties in relation to the periodic table.


Dr. George E. Miller is senior lecturer SOE emeritus in the Department of Chemistry at the University of California, Irvine, where he is also the principal scientist and the reactor supervisor of UCI's nuclear reactor and faculty director for science education programs at UCI's Center for Educational Partnership, including Faculty Outreach Collaborations Uniting Scientists, Students and Schools (FOCUS). He was a member and chair of the AP Chemistry Development Committee and is currently a member of the College Board Subject Test in Chemistry Development Committee. He has been a Reader, Table Leader, and Question Leader for AP Chemistry.