6.1 ∣ The Wave Nature of Light

• Much of our present understanding of the electronic structure of atoms has come from analysis of the light either emitted or absorbed by substances. The light we see with our eyes, visible light, is one type of electromagnetic radiation. Because electromagnetic radiation carries energy through space, it is also known as radiant energy.

• All types of electromagnetic radiation move through a vacuum at 2.998 * 108 m^s, the speed of light.

• The distance between two adjacent peaks (or between two adjacent troughs) is called the

• wavelength.

• The number of complete wavelengths, or cycles, that pass a given point each second is the frequency of the wave.

• All electromagnetic radiation moves at the same speed, namely, the speed of light.

• The various types of electromagnetic radiation arranged in order of increasing wavelength, a display called the electromagnetic spectrum.

• Frequency is expressed in cycles per second, a unit also called a hertz (Hz).

6.2 ∣ Quantized Energy and Photons

• (1) the emission of light from hot objects (referred to as blackbody radiation because the objects studied appear black before heating), (2) the emission of electrons from metal surfaces on which light shines (the photoelectric effect), and (3) the emission of light from electronically excited gas atoms (emission spectra).

Hot Objects and the Quantization of Energy

Max Planck (1858–1947)

• German physicist.

• Solved the problem by making a daring assumption: He proposed that energy can be either released or absorbed by atoms only in discrete “chunks” of some minimum size.

• Name quantum (meaning “fixed amount”) to the smallest quantity of energy that can be emitted or absorbed as electromagnetic radiation.

• The constant h is called the Planck constant and has a value of 6.626 * 10^- 34 joule second (Js).

Planck's theory states that matter can produce and absorb energy only in whole number multiples of hn, such as hn, 2hn, 3hn, etc. An atom emits three quanta of energy if its energy output is 3hn. Quantized energies are those that can only be emitted in particular amounts. Planck won the 1918 Nobel Prize in Physics for his groundbreaking quantum theory.

The Photoelectric Effect and Photons

In 1905, Albert Einstein (1879– 1955) used Planck’s theory to explain the photoelectric effect.

• To explain the photoelectric effect, Einstein assumed that the radiant energy striking the metal surface behaves like a stream of tiny energy packets. Each packet, which is like a “particle” of energy, is called a photon.

• Energy of photon = E = hv

• A certain amount of energy—called the work function—is required for the electrons to overcome the attractive forces holding them in the metal.

• Electrons cannot escape from metal if photons impacting it have less energy than the work function. Only changing the light frequency emits electrons from the metal, not increasing its intensity. The number of photons striking the surface per unit time determines light intensity, not photon energy. Electrons are emitted when photon energy exceeds the metal's work function.

• Einstein won the Nobel Prize in Physics in 1921 primarily for his explanation of the photoelectric effect.

6.3 ∣ Line Spectra and the Bohr Model

• In 1913, the Danish physicist Niels Bohr offered a theoretical explanation of line spectra, another phenomenon that had puzzled scientists during the nineteenth century.

• Radiation composed of a single wavelength is monochromatic.

• A spectrum is produced when radiation from a polychromatic source is separated into its component wavelengths.

• This rainbow of colors, containing light of all wavelengths, is called a continuous spectrum.

• Creating a spectrum. A continuous visible spectrum is produced when a narrow beam of white light is passed through a prism. The white light could be sunlight or light from an incandescent lamp.

• Atomic emission of hydrogen and neon. Different gases emit light of different characteristic colors when an electric current is passed through them.

• Line spectra of hydrogen and neon. The colored lines occur at wavelengths present in the emission. The black regions are wavelengths for which no light is produced in the emission.

• A spectrum containing radiation of only specific wavelengths is called a line spectrum.

Bohr’s Model

• Bohr assumed that electrons in hydrogen atoms move in circular orbits around the nucleus, but this assumption posed a problem. According to classical physics, a charged particle (such as an electron) moving in a circular path should continuously lose energy.

Bohr based his model on three postulates:

1. Only orbits of certain radii, corresponding to certain specific energies, are permitted for the electron in a hydrogen atom.

2. An electron in a permitted orbit is in an “allowed” energy state. An electron in an allowed energy state does not radiate energy and, therefore, does not spiral into the nucleus.

3. Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy state to another. This energy is emitted or absorbed as a photon that has energy E = hn.

The Energy States of the Hydrogen Atom

• The integer n, which can have whole-number values of 1, 2, 3, ...∞, is called the principal quantum number.

• The higher one climbs (the greater the value of n), the higher the energy. The lowest-energy state (n = 1, analogous to the bottom rung) is called the ground state of the atom.

• When the electron is in a higher-energy state (n = 2 or higher), the atom is said to be in an excited state.

• The state in which the electron is completely separated from the nucleus is called the reference, or zero-energy, state of the hydrogen atom.

• In his third postulate, Bohr assumed that the electron can "jump" from one permitted orbit to another by absorbing or releasing photons whose radiant energy matches the energy difference between the orbits.

• When ∆E is negative, a photon is emitted as the electron falls to a lower-energy level.

Limitations of the Bohr Model

• What is most significant about Bohr’s model is that it introduces two important ideas that are also incorporated into our current model:

1. Electrons exist only in certain discrete energy levels, which are described by quantum numbers.

2. Energy is involved in the transition of an electron from one level to another.

6.4 ∣ The Wave Behavior of Matter

• Louis de Broglie (1892–1987), who was working on his Ph.D. thesis in physics at the Sorbonne in Paris, boldly extended this idea: If radiant energy could, under appropriate conditions, behave as though it were a stream of particles (photons), could matter, under appropriate conditions, possibly show the properties of a wave?

• A= h/mv

• The quantity mv for any object is called its momentum. De Broglie used the term matter waves to describe the wave characteristics of material particles.

• Electron wave qualities were empirically confirmed several years after de Broglie's theory.

• X-ray diffraction occurs when X-rays pass through a crystal, creating a wave-like interference pattern. Electrons diffract in crystals. Thus, electrons behave like X rays and all other electromagnetic waves.

• In the electron microscope, for instance, the wave characteristics of electrons are used to obtain images at the atomic scale.

The Uncertainty Principle

Werner Heisenberg

• German physicist.

• Proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of an object at a given instant.

• Heisenberg’s principle is called the uncertainty principle.

• De Broglie's hypothesis and Heisenberg's uncertainty principle paved the way for a more general atomic structure theory. This technique abandons attempts to define the electron's instantaneous location and momentum. Electrons behave like waves because they are waves. The model accurately describes electron energy but probabilistically characterizes its position.

6.5 ∣ Quantum Mechanics and Atomic Orbitals

Erwin Schrödinger (1887–1961)

• Austrian physicist.

• Proposed an equation, now known as Schrödinger’s wave equation, that incorporates both the wave-like and particle-like behaviors of the electron.

• Schrödinger treated the electron in a hydrogen atom like the wave on a plucked guitar string.

• Because such waves do not travel in space, they are called standing waves.

• Solving Schrödinger’s equation for the hydrogen atom leads to a series of mathematical functions called wave functions that describe the electron in the atom.

• According to the uncertainty principle, if we know the momentum of the electron with high accuracy, our simultaneous knowledge of its location is very uncertain.

Orbitals and Quantum Numbers

• The solution to Schrödinger’s equation for the hydrogen atom yields a set of wave functions called orbitals.

• An orbital (quantum-mechanical model, which describes electrons in terms of probabilities, visualized as “electron clouds”) is not the same as an orbit (the Bohr model, which visualizes the electron moving in a physical orbit, like a planet around a star).

1. The principal quantum number, n, can have positive integral values 1, 2, 3, . . . . As n increases, the orbital becomes larger, and the electron spends more time farther from the nucleus. An increase in n also means that the electron has a higher energy and is therefore less tightly bound to the nucleus.

2. The second quantum number—the angular momentum quantum number, l— can have integral values from 0 to (n - 1) for each value of n. This quantum number defines the shape of the orbital.

3. The magnetic quantum number, ml, can have integral values between -l and l, including zero.

• The collection of orbitals with the same value of n is called an electron shell.

• The set of orbitals that have the same n and l values is called a subshell.

6.6 ∣ Representations of Orbitals

The S Orbitals

• The first thing we notice about the electron density for the 1s orbital is that it is spherically symmetric—in other words, the electron density at a given distance from the nucleus is the same regardless of the direction in which we proceed from the nucleus.

• The distance from the nucleus—each resulting curve is the radial probability function for the orbital.

• The number of peaks, the number of points at which the probability function goes to zero (called nodes), and how spread out the distribution is, which gives a sense of the size of the orbital.

Comparing the radial probability distributions for the 1s, 2s, and 3s orbitals reveals three trends:

1. For an ns orbital, the number of peaks is equal to n, with the outermost peak being larger than inner ones.

2. For an ns orbital, the number of nodes is equal to n - 1.

3. As n increases, the electron density becomes more spread out; that is, there is a greater prob- ability of finding the electron further from the nucleus.

The p Orbitals

• Each p subshell has three orbitals, corresponding to the three allowed values of ml: -1, 0, and 1.

• The electron density is not distributed spherically as in an s orbital.

• For each value of n, the three p orbitals have the same size and shape but differ from one another in spatial orientation.

The d and f Orbitals

• The different d orbitals in a given shell have different shapes and orientations in space.

• Four of the d-orbital contour representations have a “four-leaf clover” shape, with four lobes, and each lies primarily in a plane.

• The shapes of the f orbitals are even more complicated than those of the d orbitals and are not presented here.

6.7 ∣ Many-Electron Atoms

Orbitals and Their Energies

• Although the shapes of the orbitals of a many-electron atom are the same as those for hydrogen, the presence of more than one electron greatly changes the energies of the orbitals.

• In a many-electron atom, however, the energies of the various subshells in a given shell are different because of electron–electron repulsions.

• Orbitals with the same energy are said to be degenerate.

• Qualitative energy-level diagram; the exact energies of the orbitals and their spacings differ from one atom to another.

• Qualitative energy-level diagram; the exact energies of the orbitals and their spacings differ from one atom to another.

Electron Spin and the Pauli Exclusion Principle

• In 1925, the Dutch physicists George Uhlenbeck (1900–1988) and Samuel Goudsmit (1902–1978) proposed a solution to this dilemma. They postulated that electrons have an intrinsic property, called electron spin, that causes each electron to behave as if it were a tiny sphere spinning on its own axis.

• This new quantum number, the spin magnetic quantum number, is denoted ms (the subscript s stands for spin).

• In 1925, the Austrian-born physicist Wolfgang Pauli (1900–1958) discovered the principle that governs the arrangement of electrons in many-electron atoms. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers.

• An orbital can hold a maximum of two electrons and they must have opposite spins.

6.8 ∣ Electron Configurations

• The way electrons are distributed among the various orbitals of an atom is called the electron configuration of the atom. The most stable electron configuration—the ground state—is that in which the electrons are in the lowest possible energy states.

• The orbitals are filled in order of increasing energy, with no more than two electrons per orbital.

• The 1s orbital can accommodate two of the electrons. The third one goes into the next lowest-energy orbital, the 2s.

• The Pauli exclusion principle tells us, however, that there can be at most two electrons in any single orbital.

• Electrons having opposite spins are said to be paired when they are in the same orbital.

• An unpaired electron is one not accompanied by a partner of opposite spin.

Hund’s Rule

• Hydrogen has one electron, which occupies the 1s orbital in its ground state.

• Helium, The next element, helium, has two electrons.

• Lithium, The electron configurations of lithium and several elements that follow it in the periodic table.

• Beryllium and Boron, The element that follows lithium is beryllium; its electron configuration is 1s^2,2s^2.

• Carbon, the sixth electron must go into a 2p orbital.

• Hund’s rule states that that when filling degenerate orbitals the lowest energy is attained when the number of electrons having the same spin is maximized.

Condensed Electron Configurations

• In writing the condensed electron configuration of an element, the electron configuration of the nearest noble-gas element of lower atomic number is represented by its chemical symbol in brackets.

• We refer to the electrons represented by the bracketed symbol as the noble-gas core of the atom. More usually, these inner-shell electrons are referred to as the core electrons.

• The electrons given after the noble-gas core are called the outer-shell electrons.

• The outer-shell electrons include the electrons involved in chemical bonding, which are called the valence electrons.

Transition Metals

• In all its chemical properties, potassium is clearly a member of the alkali metal group.

• the fourth row of the periodic table is ten elements wider than the two previous rows. These ten elements are known as either transition elements or transition metals.

The Lanthanides and Actinides

• The 14 elements corresponding to the filling of the 4f orbitals are known as either the lanthanide elements or the rare earth elements.

• The properties of the lanthanide elements are all quite similar, and these elements occur together in nature.

• The actinide elements, of which uranium (U, element 92) and plutonium (Pu, element 94) are the best known, are then built up by completing the 5f orbitals.

6.9 ∣ Electron Configurations and the Periodic Table

• The order in which electrons are added to orbitals is read left to right beginning in the top-left corner.

• The periodic table can be further divided into four blocks based on the filling order of orbitals.

• On the left are two blue columns of elements. These elements, known as the alkali metals (group 1A) and alkaline earth metals (group 2A), are those in which the valence s orbitals are being filled.

• The s block and the p block elements together are the representative elements, sometimes called the main-group elements.

• The orange block has ten columns containing the transition metals.

• The elements in the two tan rows containing 14 columns are the ones in which the valence f orbitals are being filled and make up the f block. Consequently, these elements are often referred to as the f-block metals.

• The number of columns in each block corresponds to the maximum number of electrons that can occupy each kind of subshell.

• The periodic table is your best guide to the order in which orbitals are filled.

• In general, for representative elements we do not consider the electrons in completely filled d or f subshells to be valence electrons, and for transition elements we do not consider the electrons in a completely filled f subshell to be valence electrons.