Welcome to week 14 of Science Friday. For the past few weeks, I have solely focused on concepts relating to physics. This week, I’d like to shift gears to generate some variety in my lineup. Today we are going to discuss the ever important field of chemistry—more specifically electron configurations. This is a topic I need to cover to advance to a more interesting topic next week (chemical bonds). Let’s lay out the basic groundwork. Every atom we know to exist in the universe—either naturally or by artificial means—is on the periodic table of elements. Each atom is uniquely described by its atomic number, or the number of protons it contains. Atoms also consist of neutrons (in the nucleus with the protons) and significantly less massive electrons surrounding the nucleus. The field of chemistry concerns itself primarily with the electrons of atoms, more specifically how the electrons of different atoms interact (bonds). Before we can understand this appreciably, we need to understand how electrons are distributed in an atom. This has been no small task historically; scientists have changed the structure of the atom numerous times. The model of the atom that is most commonly perpetuated by pictures is what we call the Bohr model. In this model, the nucleus is surrounded by defined orbits in which electrons reside. In essence, this model of the atom is a mini solar system. While this model has practical benefits in describing various phenomena, it is not an accurate depiction of the atom. In reality, the atom consists of a nucleus that occupies an incredibly small fraction of the volume of an atom. If a pea represents the nucleus of an atom, then an entire football stadium would represent the entire atom. Electrons do not orbit the nucleus as the Bohr model suggests, but rather “exist” at various probabilities that decrease proportional to the distance from the nucleus. These volumes of probabilities are described as “shells.” To assign a unique identifier to each electron of an atom, chemists use four quantum numbers that are the result of Schrödinger’s equation—a mathematical construct that entails advanced level calculus to appreciate fully. The four quantum numbers are the principal, angular, magnetic, and spin. Before I describe each of these quantum numbers in detail, I need to make a disclaimer. When we are describing the quantum world, we end up dealing with concepts that are counterintuitive. To compound this issue, physicists and chemists often assign adjectives to properties that we believe we can relate to. For example, chemists describe the “spin” of an electron. The notion of spin on the quantum level is nothing like the notion of spin on the macroscopic level. Spin is an inherent property in the quantum world, just like mass. The first quantum number assigned to an electron is called the principal quantum number. It describes the energy shell of the electron and can take on any integer value n greater than or equal to 1. The rows (periods) on the periodic table describe this quantum number: hydrogen and helium have valence (outermost) electrons in the n = 1 shell, while lithium, beryllium, boron, carbon, nitrogen, oxygen, etc. have valence electrons in the n = 2 shell. While we often relate greater values of n to greater distance from the nucleus, it is more accurate to think of greater values of n as greater [i]energy[/i]. Indeed, an electron further away from the positively charged nucleus has a higher potential energy than an electron closer, but this classical notion becomes confused when we deal with larger atoms. After we have specified the principal energy level of the electron, we then describe the angular quantum number. This number describes the sub-shell within a shell that an electron resides in. In unexcited atoms, there are four sub-shells we deal with: s, p, d, and f. These sub-shells are described by the angular quantum number, [i]l[/i]. [i]l[/i] can take on any value between 0 and n - 1. For example, if n = 1, then l = 0. l = 0 is the s sub-shell; l = 1 is the p sub-shell, and so forth. The order of sub-shells (s, p, d, f) is in ascending energy. Within the n = 2 shell, the p sub-shell has higher energy than the s sub-shell. Once we have assigned a sub-shell to an electron within any given atom, we need to determine which [i]orbital[/i] within that sub-shell the electron probabilistically resides in. The s sub-shell has one orbital (shown as a sphere); the p sub-shell has three orbitals (three dumbbells pointing in the x, y, and z directions); the d sub-shell has five orbitals; and the f sub-shell has seven orbitals. The specific orbital within a sub-shell is specified by the magnetic quantum number, m sub l. m sub l can take on any integer value between -l and l (which gives the 1, 3, 5, 7 pattern I noted). Finally, once we have the orbital the electron resides in as a function of a probability density, then we must assign the electron a spin. In any given orbital (specified by m sub l), only two electrons may reside. Furthermore, these two electrons must have opposite spin; this is dictated by the law of physics known as Pauli’s exclusion principle. This is fundamentally why when you place your hand on a table your hand does not pass through. The electrons in your hand cannot occupy the orbitals in the desk. So there we have it, the four quantum numbers. As we move down and across the periodic table, we can see that the number of electrons quickly becomes fairly large. In the process of chemical reactions, however, we are only interested in the electrons that are “exposed” to the environment; these are the electrons in the outermost, or valence, shell of the atom. The d sub-shell electrons are never included in the valence electron count of an atom because of the energy difference of orbitals when they are filled as opposed to when they are empty. Next week, we will discuss how the valence electrons of two atoms interact to form chemical bonds—the topic of interest. Stay tuned! If you have any questions, please leave them below. I appreciate it when readers leave general comments about the subject or post to generate discussion. These weekly posts are incredibly dull without feedback. See you next week!