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The theories describing the arrangement of protons, neutrons, and electrons within an atom were developed from various experiments. The nuclear model of the atom, proposed by Rutherford, was based on an experiment where a particles bombarded gold foil. In this model, protons and neutrons are concentrated in a very tiny fraction of the volume of the atom, called the nucleus. Electrons were somewhere outside this nucleus and taking up most of the space of an atom.

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Because electrons take up most of the space in an atom and are on the outside of an atom, most chemical properties are due to electrons. When an atom encounters another atom (chemically react), it is the electrons that interact. When an atom interacts with light, it is the electrons that respond to that energy. Consequently, much of the theory of atomic structure is devoted to the study of electrons, and most of the experimental evidence for these theories is based on the interaction of electrons with light.

The photoelectric effect is an example of the interaction of light and electrons. The photoelectric effect is a process by which some metals emit electrons when exposed to light. The light must have a minimum frequency or energy for this process to occur. If the light has this frequency, then the number of electrons emitted is proportional to the brightness of the light. Einstein explained this process by thinking of the light as a particle, called a photon, which transmits all its energy to an atom in the metal. If the energy is sufficient, an electron can escape the metal. The brightness corresponds to the number of photons, so if each photon releases one electron, brighter light will produce more electrons. The relationship between energy and frequency (or wavelength) from Chapter 1 can be used either to determine the relationship between the energy required for an electron to escape (called the work function, ) and frequency (E = h) or to find the wavelength (E = hc/).

Another interaction of electrons with light produces an absorption or emission spectrum. A spectrum is a graph of the intensity of light versus its energy or wavelength. It was experimentally observed that these spectra are different for each element. In addition, these are line spectra. Line spectra show that the interactions between light and electrons occur at specific energies. Unlike the photoelectric effect that will occur at any frequency above a threshold value, lines occur at a specific energy, disappear, and reappear at different energies. Line spectra suggest the quantum nature of electrons. In quantum theory, there are specific choices rather than any value within a range. For example, in quantum theory you may choose 1 or 2, but not 1.5 or any other fraction between 1 and 2. On the other hand, in classical theories, any choice between 1 and 2, including 1.5, would be acceptable.

                              >> Explore: Light Emission and Absorption Tutorial

Since hydrogen, with only one electron, is the simplest of all atoms, most theory was developed around its spectrum. The lines in the spectrum of hydrogen were found to follow a pattern. This pattern was

1/ = 1.097 x 10^–2 nm^–1(1/n₁² – 1/n₂²)       (Equation 3.4)

where is wavelength in nanometers and n is a counting number (1, 2, 3, etc.). Niels Bohr explained this pattern by proposing that the electrons orbit the nucleus as a planet orbits the sun. The values of n represented the orbits and the lines were due to the electron of hydrogen moving from one orbit to another. Because only specific orbits were allowed, the quantum nature of the spectra was also explained. The orbit closest to the nucleus would be lowest in energy and called the ground state. Orbits further out were higher in energy or excited states. It requires energy (the energy of a photon) to move the electron from the ground state to an excited state. Since all the energy of the photon is transferred to the electron, the energy of the photon must exactly match the energy difference between the allowed orbits. Those energies are the lines in the spectrum.

                              >> Explore: Bohr Model of the Atom Tutorial

Although the Bohr model of the atom makes a nice picture (in fact, it is the one normally used to represent an atom), it is no longer considered a good description of the behavior of electrons. There are two major reasons: (1) it only works for one-electron atoms and (2) there is no reason given for electrons to behave in that manner. Instead, the current theory to explain electrons is quantum mechanics.

Quantum mechanics assumes wave-particle duality of electrons. The properties of light are also explained with wave-particle duality. In fact, de Broglie proposed that any particle can also be treated as a wave and that the relationship between particles and waves is

= h/mv       (Equation 3.14)

where = wavelength (m), h = Planck's constant (6.626 x 10^–34 J•s), m = mass of particle (kg), and v = velocity (m/s).

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De Broglie's equation inspired Erwin Schrödinger to describe the energy of a hydrogen electron as a wave. This equation not only matched the line spectrum of hydrogen, but also gave reasons for the behavior of hydrogen. While Schrödinger's wave equation only works perfectly for hydrogen, it does work approximately for multielectron atoms, and an incredible amount of chemical behavior is explained and predicted based on his basic principles.

One problem with describing an electron as a wave is that waves are hard to picture. Instead, the square of the wave function, called the probability density, is used. A probability density is the volume of space in which the electron is likely to be found. A denser region has a higher probability of finding an electron. A region where there is zero probability of finding an electron is called a node. The space where the probability of finding an electron is high is called an orbital. One of the reasons that quantum mechanics describes electrons in terms of probability is stated in Heisenberg's uncertainty principle. This principle recognizes that making an observation sometimes changes what you are observing. The Heisenberg uncertainty principle states that is it impossible to simultaneously determine the position and momentum of an electron.

Based on Schrödinger's equation, there are three values that describe an orbital. Later, a fourth one was added. These four values, called quantum numbers, completely describe an electron. Every electron in an atom has a unique set of these four quantum numbers (Pauli exclusion principle). For each quantum number there is a set of possible values and each quantum number describes some aspect of the electron and its orbital.

The first quantum number is called the principal quantum number and is represented by n. The principal quantum number can have values of the counting numbers (1, 2, 3, etc.). It is the same n as in Equation 3.4. It describes the maximum distance from the nucleus where an electron is likely to be found. Larger values are further from the nucleus. It also describes the energy of the electron; larger values are higher in energy.

The next quantum number is the angular momentum quantum number, which has the symbol of l. The possible values of l are 0 to n – l. This means that the choices for l are limited by the value of n. The angular momentum quantum number describes the shape of the orbital. As l increases these shapes get more complicated. Usually l is described with a letter instead of a number. If l = 0, it can also be called s and it has a spherical shape. (See Figure 3.15D.) If l = 1, it can be called p, and the shape is usually described as a dumbbell. (See Figure 3.19.) If l = 2, it can be called d, and the shape is usually described as a clover, although there is one d orbital that looks different. (See Figure 3.20.) If l = 3, it is called an f orbital. These shapes are very complicated. Since f orbitals are not commonly used and atoms with l = 4 (g) haven't yet been synthesized, the details of these orbitals can generally be ignored. Increasing l also increases energy, but the energy differences are smaller than energy difference associated with n.

The third quantum number is the magnetic quantum number. Its symbol is m_l. This quantum number has integer values from –l to +l (including zero). It describes the orientation of the orbital. At this point, it is more important to determine how many possible orientations are available than what those orientations are. For an s orbital (l = 0), the only possible value of m_l is zero. Therefore there is only one orientation of an s orbital. If l = 1 (p orbital), m_l has values of –1, 0, and +1, so there are three possible orientations. There are five orientations of d orbitals and seven orientations of f orbitals. There is no energy difference with orientation, so the orientations of orbitals of each type are called degenerate.

The fourth quantum number is the spin quantum number, which has the symbol of m_s. It may have a value of +1/2 or –1/2. It describes the spin of an electron within the orbital. Consequently, each orientation of each orbital can contain two electrons, provided those electrons are spinning in opposite directions. Another common way to represent oppositely spinning electrons is with up and down arrows.

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In multielectron atoms, the electrons will prefer the lowest-energy orbital available. The list of electrons in each orbital is called the electron configuration. For example, the electron configuration of nickel is 1s²2s²2p⁶3s²3p⁶4s²3d⁸. The first number represents the value of n; the letter, the value of l; and the superscripted number, the number of electrons in that orbital. The s orbital only has one orientation since two electrons fit in that orbital; the superscript is a 2. The p orbital has three orientations, with two in each; it can contain a maximum of six electrons. As the electrons fill the orbital, the first three electrons go into orbitals with different orientations. All these electrons spin in the same direction. This fulfills Hund's rule, which says that the lowest energy is for electrons to exist in separate orbitals with parallel spins. Although the energy difference for l quantum numbers is smaller than that for n quantum numbers, several small steps turn out to be higher in energy than one large step.

                              >> Explore: Electron Configuration Tutorial

Consequently, the 4s energy level is lower than the 3d level. A useful rule for comparing energies is that the lowest n + l will have the lowest energy. If n + l is the same for two orbitals, the one with the lower n will be lower in energy. While d orbitals may contain a maximum of 10 electrons, nickel only has a total of 28 electrons, so there are no more electrons to add to the d orbital. Hund's rule says that those eight electrons will be distributed as . The number of unpaired electrons is important to the magnetic properties of an element. Only electrons in the highest-energy orbital might be unpaired, and this value can be determined from the number of possible orientations and Hund's rule. For the example of nickel, there are two unpaired electrons.

Although it was developed separately, the periodic table turns out to be an excellent predictor of electron configurations and chemical properties related to electron configuration. It is organized into rows and columns. The rows of a periodic table are called periods. The highest value of n in the electron configuration of an element will be the same for all elements in that period. The columns of the periodic table are called groups or families. Elements in a column have similar chemical properties. The number of electrons and their pattern with l values in the highest-energy orbitals are the same for each element in a column. This is consistent with the idea that the arrangement of electrons determines the chemical properties. Some groups of elements are named. The group at the far right of the periodic table (which includes Ne and Ar) is called the noble gases. These elements have s and p orbitals that are completely full. Since this is an especially stable (low-energy) arrangement, noble gases tend not to combine with other elements. If the highest-energy electron is in a d orbital, the element is part of a group called the transition metals. Elements where the highest-energy electron is in the 4f orbital are called lanthanides, or rare earth elements. Elements where the highest-energy electron is in a 5f orbital are called actinide elements.

One of the chemical properties that shows a periodic trend is ionization energy. Ionization energy is the energy required to remove an electron from an atom in the gaseous state. What holds the electron to the atom is the force between the positive charge of the nucleus and the negative electron. As the electrons get further from the nucleus, this force decreases. In addition, there are electrons between the nucleus and the outermost electron, shielding the nuclear charge from the outermost electron. The actual force felt by the outermost electron is called the effective nuclear charge (Z_eff). The outermost electron of elements lower in the periodic table will be further from the nucleus (n is larger) and more shielded by other electrons. Therefore it is easier to remove the electron and the ionization energy is lower. Since elements in the same period have the same maximum value of n, each will be the same distance from the nucleus. However, elements on the left of the periodic table have fewer protons than elements on the right. Consequently, ionization energy increases from left to right across the periodic table. There is one reversal of this general trend. Elements with a p⁴ configuration tend to have slightly lower ionization energies than elements with a p³ configuration. A p³ element has one electron in each orientation of the p orbitals. This is a particularly stable arrangement of electrons. Since removing one electron from a p⁴ creates this organization, it requires less energy than disrupting this orientation.

X-ray photoelectron spectroscopy (XPS) also shows a periodic trend. In XPS, X-rays are used to remove electrons from an atom. The X-rays are sufficiently energetic to remove inner-shell electrons as well as outer-shell electrons. A graph of the energy of the X-rays versus signal (which is proportional to the number of electrons ejected) shows the same pattern as an electron configuration.