Chapter 6 Electronic Structure of Atoms Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapter 6 Electronic Structure of Atoms John D. Bookstaver St. Charles Community College Cottleville, MO © 2009, Prentice-Hall, Inc.

6.1 The WAVE NATURE OF LIGHT P.211-215 HW: 6.9, 6.10, 6.12, 6.16, 6.18, 6.20, 6.22, 6.26, 6.30 © 2009, Prentice-Hall, Inc.

6.1 The Wave Nature of Light The electronic structure of an atom refers to the arrangement of electrons. Visible light is a form of electromagnetic radiation or radiant energy. Radiation carries energy through space. Electromagnetic radiation is characterized by its wave nature. © 2009, Prentice-Hall, Inc.

Waves To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. The distance between corresponding points on adjacent waves is the wavelength (). All waves have a characteristic wavelength,  (lambda), and amplitude, A. © 2009, Prentice-Hall, Inc.

Waves The number of waves passing a given point per unit of time is the frequency (). For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. © 2009, Prentice-Hall, Inc.

Electromagnetic Radiation All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  108 m/s. Therefore, c =  C = the speed of light = frequency  = wavelength The frequency,  (nu), of a wave is the number of cycles which pass a point in one second. The units of  are Hertz (1 Hz = 1 s–1). The speed of a wave is given by its frequency multiplied by its wavelength. Electromagnetic radiation moves through a vacuum with a speed of 3.00 x 108 m/s. © 2009, Prentice-Hall, Inc.

Sample Exercise 6.1 Concepts of Wavelength and Frequency Two electromagnetic waves are represented below. (a) Which wave has the higher frequency? (b) If one wave represents visible light and the other represents infrared radiation, which wave is which? Solution (a) The lower wave has a longer wavelength (greater distance between peaks). The longer the wavelength, the lower the frequency (v = c/λ). Thus, the lower wave has the lower frequency, and the upper wave has the higher frequency. (b) The electromagnetic spectrum (Figure 6.4) indicates that infrared radiation has a longer wavelength than visible light. Thus, the lower wave would be the infrared radiation. If one of the waves in the margin represents blue light and the other red light, which is which? Answer: The expanded visible-light portion of Figure 6.4 tells you that red light has a longer wavelength than blue light. The lower wave has the longer wavelength (lower frequency) and would be the red light. Practice Exercise

Sample Exercise 6.2 Calculating Frequency from Wavelength The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation? A laser used in eye surgery to fuse detached retinas produces radiation with a wavelength of 640.0 nm. Calculate the frequency of this radiation. An FM radio station broadcasts electromagnetic radiation at a frequency of 103.4 MHz (megahertz; MHz = 106 s–1). Calculate the wavelength of this radiation. The speed of light is 2.998 × 10^8 m/s to four significant digits. Answers: (a) 4.688 × 1014 s–1, (b) 2.901 m

6.2 Quantized Energy & Photons © 2009, Prentice-Hall, Inc.

6.2 Quantized Energy and Photons Some phenomena can’t be explained using a wave model of light: Blackbody radiation is the emission of light from hot objects. The photoelectric effect is the emission of electrons from metal surfaces on which light shines. Emission spectra are the emissions of light from electronically excited gas atoms. © 2009, Prentice-Hall, Inc.

Hot Objects and the Quantization of Energy The wave nature of light does not explain how an object can glow when its temperature increases. Heated solids emit radiation (black body radiation) The wavelength distribution depends on the temperature (i.e., “red hot” objects are cooler than “white hot” objects). Max Planck explained it by assuming that energy comes in packets called quanta. © 2009, Prentice-Hall, Inc.

Hot Objects and the Quantization of Energy Planck proposed that energy can only be absorbed or released from atoms in certain amounts. These amounts are called quanta. A quantum is the smallest amount of energy that can be emitted or absorbed as electromagnetic radiation. © 2009, Prentice-Hall, Inc.

Hot Objects and the Quantization of Energy The relationship between energy and frequency is: E = h where h is Planck’s constant (6.626 x 10–34 J-s). © 2009, Prentice-Hall, Inc.

The Nature of Energy Einstein used this assumption to explain the photoelectric effect. He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.626  10−34 J-s. © 2009, Prentice-Hall, Inc.

The Nature of Energy Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c =  E = h © 2009, Prentice-Hall, Inc.

The Nature of Energy Another mystery in the early 20th century involved the emission spectra observed from energy emitted by atoms and molecules. © 2009, Prentice-Hall, Inc.

Sample Exercise 6.3 Energy of a Photon Calculate the energy of one photon of yellow light with a wavelength of 589 nm. Solution Analyze: Our task is to calculate the energy, E, of a photon, given λ = 589 nm. This is the magnitude of enthalpies of reactions (Section 5.4), so radiation can break chemical bonds, producing what are called photochemical reactions.

Answers: (a) 3.11 × 10–19 J, (b) 0.16 J, (c) 4.2 × 1016 photons Sample Exercise 6.3 Energy of a Photon A laser emits light with a frequency of 4.69 × 1014 s–1. What is the energy of one photon of the radiation from this laser? If the laser emits a pulse of energy containing 5.0 × 1017 photons of this radiation, what is the total energy of that pulse? If the laser emits 1.3 × 10–2 J of energy during a pulse, how many photons are emitted during the pulse? Answers: (a) 3.11 × 10–19 J, (b) 0.16 J, (c) 4.2 × 1016 photons Practice Exercise

6.3 Line Spectra and the Bohr Model Pp. 218-222 © 2009, Prentice-Hall, Inc.

Radiation composed of only one wavelength is called monochromatic. Radiation that spans a whole array of different wavelengths is called continuous. © 2009, Prentice-Hall, Inc.

Line Spectra When radiation from a light source, such as a lightbulb, is separated into its different wavelength components, a spectrum is produced. White light can be separated into a continuous spectrum of colors. A rainbow is a continuous spectrum of light produced by the dispersal of sunlight by raindrops or mist. On the continuous spectrum there are no dark spots which would correspond to different lines. © 2009, Prentice-Hall, Inc.

Line Spectra Not all radiation is continuous. A gas placed in a partially evacuated tube and subjected to a high voltage produces single colors of light. The spectrum that we see contains radiation of only specific wavelengths; this is called a line spectrum. © 2009, Prentice-Hall, Inc.

Bohr’s Model Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: Electrons in an atom can only occupy certain orbits (corresponding to certain energies). © 2009, Prentice-Hall, Inc.

Bohr’s Model Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. © 2009, Prentice-Hall, Inc.

Bohr’s Model Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h © 2009, Prentice-Hall, Inc.

The Nature of Energy The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: E = −RH ( ) 1 nf2 ni2 - where RH is the Rydberg constant, 2.18  10−18 J, and ni and nf are the initial and final energy levels of the electron. © 2009, Prentice-Hall, Inc.

The Energy States of the Hydrogen Atom Colors from excited gases arise because electrons move between energy states in the atom. Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra. © 2009, Prentice-Hall, Inc.

The Energy States of the Hydrogen Atom Bohr showed mathematically that where n is the principal quantum number (i.e., n = 1, 2, 3, … ) and RH is the Rydberg constant. The product hcRH = 2.18 x 10-18 J. © 2009, Prentice-Hall, Inc.

The Energy States of the Hydrogen Atom The first orbit in the Bohr model has n = 1 and is closest to the nucleus. The furthest orbit in the Bohr model has n =  and corresponds to E = 0. Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (E = hn). The ground state is the lowest energy state. An electron in a higher energy state is said to be in an excited state. © 2009, Prentice-Hall, Inc.

The Energy States of the Hydrogen Atom The amount of energy absorbed or emitted by moving between states is given by . © 2009, Prentice-Hall, Inc.

Limitations of the Bohr Model The Bohr Model has several limitations: It cannot explain the spectra of atoms other than hydrogen. Electrons do not move about the nucleus in circular orbits. However, the model introduces two important ideas: The energy of an electron is quantized: electrons exist only in certain energy levels described by quantum numbers. Energy gain or loss is involved in moving an electron from one energy level to another © 2009, Prentice-Hall, Inc.

6.4 THE WAVE BEHAVIOR OF LIGHT Pp 222-224 © 2009, Prentice-Hall, Inc.

The Wave Nature of Matter Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. Using Einstein’s and Planck’s equations, deBroglie derived: that the relationship between mass and wavelength was  = h mv © 2009, Prentice-Hall, Inc.

Sample Exercise 6.5 Matter Waves What is the wavelength of an electron moving with a speed of 5.97 × 106 m/s? The mass of the electron is 9.11 × 10–31 kg. Solution Comment: By comparing this value with the wavelengths of electromagnetic radiation shown in Figure 6.4, we see that the wavelength of this electron is about the same as that of X-rays.

3. The momentum, mn, is a particle property, whereas l is a wave property. Matter waves is the term used to describe wave characteristics of material particles. Therefore, in one equation deBroglie summarized the concepts of waves and particles as they apply to low-mass, high-speed objects. As a consequence of deBroglie’s discovery, we now have techniques such as X-ray diffraction and electron microscopy to study small objects. © 2009, Prentice-Hall, Inc.

The Uncertainty Principle Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! (x) (mv)  h 4 © 2009, Prentice-Hall, Inc.

6.5 QUANTUM MECHANICS AND ATOMIC ORBITALS © 2009, Prentice-Hall, Inc.

Quantum Mechanics Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. It is known as quantum mechanics. © 2009, Prentice-Hall, Inc.

Quantum Mechanics The wave equation is designated with a lower case Greek psi (). The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. © 2009, Prentice-Hall, Inc.

Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. Each orbital describes a spatial distribution of electron density. An orbital is described by a set of three quantum numbers. © 2009, Prentice-Hall, Inc.

Principal Quantum Number (n) The principal quantum number, n, describes the energy level on which the orbital resides. As n becomes larger, the atom becomes larger and the electron is further from the nucleus The values of n are integers ≥ 1. © 2009, Prentice-Hall, Inc.

Angular Momentum Quantum Number (l) This quantum number defines the shape of the orbital. Allowed values of l are integers ranging from 0 to n − 1. We usually use letters for l (s, p, d, and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d, and f orbitals. © 2009, Prentice-Hall, Inc.

Angular Momentum Quantum Number (l) Value of l 1 2 3 Type of orbital s p d f © 2009, Prentice-Hall, Inc.

Magnetic Quantum Number (ml) This quantum number depends on l. The magnetic quantum number describes the three-dimensional orientation of the orbital. Allowed values of ml are integers ranging from -l to l: −l ≤ ml ≤ l. 4. Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc. © 2009, Prentice-Hall, Inc.

Magnetic Quantum Number (ml) A collection of orbitals with the same value of n is called an electron shell . Different orbital types within a shell (the same n and l ) are called subshells or sublevels. There are n2 orbitals in a shell described by a the n value. For example, for n = 3, there are 32 = 9 orbitals. © 2009, Prentice-Hall, Inc.

Relationship among Values of n, l, &Ml through n = 4 © 2009, Prentice-Hall, Inc.

Sample Exercise 6.6 Subshells of the Hydrogen Atom (a) Without referring to Table 6.2, predict the number of subshells in the fourth shell, that is, for n = 4. (b) Give the label for each of these subshells. (c) How many orbitals are in each of these subshells? (a)There are four subshells in the fourth shell, corresponding to the four possible values of l (0, 1, 2, and 3). (b) These subshells are labeled 4s, 4p, 4d, and 4f. The number given in the designation of a subshell is the principal quantum number, n; the letter designates the value of the angular momentum quantum number, l: for l = 0, s; for l = 1, p; for l = 2, d; for l = 3, f. (c) There is one 4s orbital (when l = 0, there is only one possible value of ml: 0). There are three 4p orbitals (when l = 1, there are three possible values of ml: 1, 0, and –1). There are five 4d orbitals (when l = 2, there are five allowed values of ml: 2, 1, 0, –1, –2). There are seven 4f orbitals (when l = 3, there are seven permitted values of ml: 3, 2, 1, 0, –1, –2, –3). (a) What is the designation for the subshell with n = 5 and l = 1? (b) How many orbitals are in this subshell? (c) Indicate the values of ml for each of these orbitals. Answers: (a) 5p; (b) 3; (c) 1, 0, –1 Practice Exercise

6.6 REPRESENTATIONS OF ORBITALS © 2009, Prentice-Hall, Inc.

s Orbitals The value of l for s orbitals is 0. They are spherical in shape. The radius of the sphere increases with the value of n. © 2009, Prentice-Hall, Inc.

s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron. © 2009, Prentice-Hall, Inc.

p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them. © 2009, Prentice-Hall, Inc.

d Orbitals The value of l for a d orbital is 2. Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center. © 2009, Prentice-Hall, Inc.

Energies of Orbitals For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. That is, they are degenerate. © 2009, Prentice-Hall, Inc.

6.7 ENERGIES OF ORBITALS © 2009, Prentice-Hall, Inc.

6.7 Energies of Orbitals As the number of electrons increases, though, so does the repulsion between them. Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate. © 2009, Prentice-Hall, Inc.

Spin Quantum Number, ms In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. The “spin” of an electron describes its magnetic field, which affects its energy. © 2009, Prentice-Hall, Inc.

Spin Quantum Number, ms This led to a fourth quantum number, the spin quantum number, ms. The spin quantum number has only 2 allowed values: +1/2 and −1/2. © 2009, Prentice-Hall, Inc.

Pauli Exclusion Principle Pauli’s exclusion principle states that no two electrons can have the same set of four quantum numbers. Two electrons in the same orbital must have opposite spins. Therefore, no two electrons in the same atom can have identical sets of quantum numbers. © 2009, Prentice-Hall, Inc.

6.8 ELECTRON CONFIGURATIONS © 2009, Prentice-Hall, Inc.

6.8 Electron Configurations Electron configurations tell us how the electrons are distributed among the various orbitals of an atom. The most stable configuration, or ground state, is that in which the electrons are in the lowest possible energy state. © 2009, Prentice-Hall, Inc.

6.8 Electron Configurations When writing ground-state electronic configurations: electrons fill orbitals in order of increasing energy with no more than two electrons per orbital. no two electrons can fill one orbital with the same spin (Pauli). for degenerate (same energy) orbitals, electrons fill each orbital singly before any orbital gets a second electron. © 2009, Prentice-Hall, Inc.

6.8 Electron Configurations How do we show spin? An arrow pointing upwards has ms = + 1/2 (spin up). An arrow pointing downwards has ms = – 1/2 (spin down). © 2009, Prentice-Hall, Inc.

Electron Configurations This shows the distribution of all electrons in an atom. Each component consists of A number denoting the energy level, © 2009, Prentice-Hall, Inc.

Electron Configurations This shows the distribution of all electrons in an atom Each component consists of A number denoting the energy level, A letter denoting the type of orbital, © 2009, Prentice-Hall, Inc.

Electron Configurations This shows the distribution of all electrons in an atom. Each component consists of A number denoting the energy level, A letter denoting the type of orbital, A superscript denoting the number of electrons in those orbitals. © 2009, Prentice-Hall, Inc.

Orbital Diagrams Each box in the diagram represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the relative spin of the electron. © 2009, Prentice-Hall, Inc.

Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.” Thus, electrons fill each orbital singly with their spins parallel before any orbital gets a second electron. By placing electrons in different orbitals, electron–electron repulsions are minimized © 2009, Prentice-Hall, Inc.

Sample Exercise 6.7 Orbital Diagrams and Electron Configurations Draw the orbital diagram for the electron configuration of oxygen, atomic number 8. How many unpaired electrons does an oxygen atom possess? Analyze and Plan: Because oxygen has an atomic number of 8, each oxygen atom has 8 electrons. Figure 6.25 shows the ordering of orbitals. The electrons (represented as arrows) are placed in the orbitals (represented as boxes) beginning with the lowest-energy orbital, the 1s. Each orbital can hold a maximum of two electrons (the Pauli exclusion principle). Because the 2p orbitals are degenerate, we place one electron in each of these orbitals (spin-up) before pairing any electrons (Hund’s rule). Solve: Two electrons each go into the 1s and 2s orbitals with their spins paired. This leaves four electrons for the three degenerate 2p orbitals. Following Hund’s rule, we put one electron into each 2p orbital until all three orbitals have one electron each. The fourth electron is then paired up with one of the three electrons already in a 2p orbital, so that the representation is The corresponding electron configuration is written 1s22s22p4. The atom has two unpaired electrons © 2009, Prentice-Hall, Inc.

Condensed Electron Configurations Electron configurations may be written using a shorthand notation (condensed electron configuration): Write the valence electrons explicitly. Valence electrons are electrons in the outer shell. These electrons are gained and lost in reactions. Write the core electrons corresponding to the filled noble gas in square brackets. Core electrons are electrons in the inner shells. These are generally not involved in bonding. © 2009, Prentice-Hall, Inc.

Condensed Electron Configurations Example: P is 1s22s22p63s23p3, but Ne is 1s22s22p6. Therefore, P is [Ne]3s23p3 © 2009, Prentice-Hall, Inc.

Transition Metals After Ar, the 4s orbital fills then the 3d orbitals begin to fill. After the 3d orbitals are full the 4p orbitals begin to fill. The 10 elements between Sc and Zn are called the transition metals or transition elements © 2009, Prentice-Hall, Inc.

The Lanthanides and Actinides The 4f orbitals begin to fill with Ce. Note: The electron configuration of La is [Xe]6s25d1. The 4f orbitals are filled for the elements Ce – Lu which are called lanthanide elements (or rare earth elements). The 5f orbitals are filled for the elements Th – Lr which are called actinide elements. Most actinides are not found in nature. © 2009, Prentice-Hall, Inc.

6.9 Electron Configurations & the Periodic Table © 2009, Prentice-Hall, Inc.

The Periodic Table The periodic table can be used as a guide for electron configurations. The period number is the value of n. Groups 1A and 2A have their s orbitals being filled. Groups 3A–8A have their p orbitals being filled. © 2009, Prentice-Hall, Inc.

The Periodic Table The lanthanides and actinides have their f orbitals being filled. The actinides and lanthanide elements are collectively referred to as the f-block metals. Note that the 3d orbitals fill after the 4s orbital. Similarly, the 4f orbitals fill after the 5d orbitals © 2009, Prentice-Hall, Inc.

Periodic Table We fill orbitals in increasing order of energy. Different blocks on the periodic table (shaded in different colors in this chart) correspond to different types of orbitals. © 2009, Prentice-Hall, Inc.

Some Anomalies Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. © 2009, Prentice-Hall, Inc.

Some Anomalies For instance, the electron configuration for copper is [Ar] 4s1 3d10 rather than the expected [Ar] 4s2 3d9. © 2009, Prentice-Hall, Inc.

Some Anomalies This occurs because the 4s and 3d orbitals are very close in energy. These anomalies occur in f-block atoms, as well. © 2009, Prentice-Hall, Inc.