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Lecture Presentation Chapter 6 Electronic Structure of Atoms © 2015 Pearson Education, Inc. James F. Kirby Quinnipiac University Hamden, CT Electronic Structure of Atoms Electronic Structure • This chapter is all about electronic structure—the arrangement and energy of electrons. • It may seem odd to start by talking about waves. However, extremely small particles have properties that can only be explained in this manner! Electronic Structure of Atoms © 2015 Pearson Education, 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 (). © 2015 Pearson Education, Inc. Electronic Structure of Atoms 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. • If the time associated with the lines to the left is one second, then the frequencies would be 2 s–1 and 4 s–1, Electronic respectively. Structure of Atoms © 2015 Pearson Education, Inc. Electromagnetic Radiation • All electromagnetic radiation travels at the same velocity: The speed of light (c) is 3.00 108 m/s. c = Electronic Structure of Atoms © 2015 Pearson Education, Inc. Sample Exercise 6.1 Concepts of Wavelength and Frequency Two electromagnetic waves are represented in the margin. (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) Wave 1 has a longer wavelength (greater distance between peaks). The longer the wavelength, the lower the frequency (ν = c ⁄ λ). Thus, Wave 1 has the lower frequency, and Wave 2 has the higher frequency. (b) The electromagnetic spectrum (Figure 6.4) indicates that infrared radiation has a longer wavelength than visible light. Thus, Wave 1 would be the infrared radiation. Electronic Structure of Atoms © 2015 Pearson Education, Inc. 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? Solution Analyze We are given the wavelength, λ, of the radiation and asked to calculate its frequency, ν. Plan The relationship between the wavelength and the frequency is given by Equation 6.1. We can solve for ν and use the values of λ and c to obtain a numerical answer. (The speed of light, c, is 3.00 × 108 m ⁄ s to three significant figures.) Solve Solving Equation 6.1 for frequency gives (ν = c ⁄ λ). When we insert the values for c and λ, we note that the units of length in these two quantities are different. We can convert the Wavelength from nanometers to meters, so the units cancel: Check The high frequency is reasonable because of the short wavelength. The units are proper because frequency has units of “per second,” or s–1. Electronic Structure of Atoms © 2015 Pearson Education, Inc. The Nature of Energy The wave nature of light does not explain how an object can glow when its temperature increases. Electronic Structure of Atoms © 2015 Pearson Education, Inc. The Nature of Energy—Quanta Max Planck explained it by assuming that energy comes in packets called quanta (singular: quantum). Electronic Structure of Atoms © 2015 Pearson Education, Inc. The Photoelectric Effect • Einstein used quanta to explain the photoelectric effect. • Each metal has a different energy at which it ejects electrons. At lower energy, electrons are not emitted. • He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.626 10−34 J∙s. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Sample Exercise 6.3 Energy of a Photon Calculate the energy of one photon of yellow light that has a wavelength of 589 nm. Solution Analyze Our task is to calculate the energy, E, of a photon, given λ = 589 nm. Plan We can use Equation 6.1 to convert the wavelength to frequency: ν=c⁄λ We can then use Equation 6.3 to calculate energy: E = hν Solve The frequency, ν, is calculated from the given wavelength, as shown in Sample Exercise 6.2: ν = c ⁄ λ = 5.09 × 1014 s–1 The value of Planck constant, h, is given both in the text and in the table of physical constants on the inside back cover of the text, and so we can easily calculate E: E = (6.626 × 10–34 J-s)(5.09 × 1014 s–1) = 3.37 × 10–19 J Comment If one photon of radiant energy supplies 3.37 × 10–19 J, we calculate that one mole of these photons will supply: (6.02 × 1023 photons ⁄ mol)(3.37 × 10–19 J ⁄ photon) = 2.03 × 105 J ⁄ mol Electronic Structure of Atoms © 2015 Pearson Education, Inc. Atomic Emissions Another mystery in the early twentieth century involved the emission spectra observed from energy emitted by atoms and molecules. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Continuous vs. Line Spectra • For atoms and molecules, one does not observe a continuous spectrum (the “rainbow”), as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed. Each element has a unique line spectrum. Electronic Structure of Atoms © 2015 Pearson Education, Inc. The Hydrogen Spectrum • Johann Balmer (1885) discovered a simple formula relating the four lines to integers. • Johannes Rydberg advanced this formula. • Neils Bohr explained why this mathematical relationship works. © 2015 Pearson Education, Inc. Electronic Structure of Atoms The Bohr Model • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies). Electronic Structure of Atoms © 2015 Pearson Education, Inc. The Bohr Model 2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. 3. 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 Electronic Structure of Atoms © 2015 Pearson Education, Inc. The Bohr Model The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation E = −hcRH ( 1 1 – n f2 ni2 ) where RH is the Rydberg constant, 1.097 107 m−1, and ni and nf are the initial and final energy levels of the electron. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Sample Exercise 6.4 Electronic Transitions in the Hydrogen Atom Using Figure 6.12, predict which of these electronic transitions produces the spectral line having the longest wavelength: n = 2 to n = 1, n = 3 to n = 2, or n = 4 to n = 3. Solution The wavelength increases as frequency decreases (λ = c ⁄ ν). Hence, the longest wavelength will be associated with the lowest frequency. According to Planck’s equation, E = hv, the lowest frequency is associated with the lowest energy. In Figure 6.12 the shortest vertical line represents the smallest energy change. Thus, the n = 4 to n = 3 transition produces the longest Electronic wavelength (lowest frequency) line. Structure of Atoms © 2015 Pearson Education, Inc. Limitations of the Bohr Model • It only works for hydrogen! • Classical physics would result in an electron falling into the positively charged nucleus. Bohr simply assumed it would not! • Circular motion is not wave-like in nature. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Important Ideas from the Bohr Model Points that are incorporated into the current atomic model include the following: 1) Electrons exist only in certain discrete energy levels. 2) Energy is involved in the transition of an electron from one level to another. Electronic Structure of Atoms © 2015 Pearson Education, Inc. The Wave Nature of Matter • Louis de Broglie theorized that if light can have material properties, matter should exhibit wave properties. • He demonstrated that the relationship between mass and wavelength was The wave nature of light is used to produce this electron micrograph. © 2015 Pearson Education, Inc. h = mv Electronic Structure of Atoms 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 Analyze We are given the mass, m, and velocity, v, of the electron, and we must calculate its de Broglie wavelength, λ. Plan The wavelength of a moving particle is given by Equation 6.8, so λ is calculated by inserting the known quantities h, m, and v. In doing so, however, we must pay attention to units. Solve Using the value of Planck constant: h = 6.626 × 10–34 J-s we have the following: Electronic Structure of Atoms © 2015 Pearson Education, Inc. The Uncertainty Principle Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position is known: h (x) (mv) 4 Electronic Structure of Atoms © 2015 Pearson Education, Inc. Quantum Mechanics • Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. • This is known as quantum mechanics. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Quantum Mechanics • The solution of Schrödinger’s wave equation is designated with a lowercase Greek psi (). • The square of the wave equation, 2, gives the electron density, or probability of where an electron is likely to be at any given time. Electronic Structure of Atoms © 2015 Pearson Education, 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. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Principal Quantum Number (n) • The principal quantum number, n, describes the energy level on which the orbital resides. • The values of n are integers ≥ 1. • These correspond to the values in the Bohr model. Electronic Structure of Atoms © 2015 Pearson Education, 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 use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Angular Momentum Quantum Number (l) Electronic Structure of Atoms © 2015 Pearson Education, Inc. Magnetic Quantum Number (ml) • 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 • Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, and so forth. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Magnetic Quantum Number (ml) • Orbitals with the same value of n form an electron shell. • Different orbital types within a shell are subshells. Electronic Structure of Atoms © 2015 Pearson Education, 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? Solution Analyze and Plan We are given the value of the principal quantum number, n. We need to determine the allowed values of l and ml for this given value of n and then count the number of orbitals in each subshell. Solve There are four subshells in the fourth shell, corresponding to the four possible values of l (0, 1, 2, and 3). 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. 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, −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). Electronic Structure of Atoms © 2015 Pearson Education, 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. Electronic Structure of Atoms © 2015 Pearson Education, Inc. s Orbitals • For an ns orbital, the number of peaks is n. • For an ns orbital, the number of nodes (where there is zero probability of finding an electron) is n – 1. • As n increases, the electron density is more spread out and there is a greater probability of finding an electron further from the nucleus. Electronic Structure of Atoms © 2015 Pearson Education, Inc. p Orbitals • The value of l for p orbitals is 1. • They have two lobes with a node between them. Electronic Structure of Atoms © 2015 Pearson Education, Inc. d Orbitals • The value of l for a d orbital is 2. • Four of the five d orbitals have four lobes; the other resembles a p orbital with a doughnut around the center. Electronic Structure of Atoms © 2015 Pearson Education, Inc. f Orbitals • Very complicated shapes (not shown in text) • Seven equivalent orbitals in a sublevel • l=3 Electronic Structure of Atoms © 2015 Pearson Education, Inc. Energies of Orbitals—Hydrogen • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. • Chemists call them degenerate orbitals. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Energies of Orbitals— Many-electron Atoms • As the number of electrons increases, so does the repulsion between them. • Therefore, in atoms with more than one electron, not all orbitals on the same energy level are degenerate. • Orbital sets in the same sublevel are still degenerate. • Energy levels start to overlap in energy (e.g., 4s is lower Electronic in energy than 3d.) Structure of Atoms © 2015 Pearson Education, 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. • This led to the spin quantum number, ms. • The spin quantum number has only two allowed values, +½ and –½. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Pauli Exclusion Principle • No two electrons in the same atom can have exactly the same energy. • Therefore, no two electrons in the same atom can have identical sets of quantum numbers. • This means that every electron in an atom must differ by at least one of the four quantum number values: n, l, ml, and ms. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Electron Configurations • The way electrons are distributed in an 5 atom is called its electron configuration. • The most stable organization is the lowest possible energy, called the ground state. • Each component consists of – a number denoting the energy level; 4p Electronic Structure of Atoms © 2015 Pearson Education, Inc. Electron Configurations 5 4p • The way electrons are distributed in an atom is called its electron configuration. • The most stable organization is the lowest possible energy, called the ground state. • Each component consists of – a number denoting the energy level; – a letter denoting the type of orbital; Electronic Structure of Atoms © 2015 Pearson Education, Inc. Electron Configurations 5 4p • The way electrons are distributed in an atom is called its electron configuration. • The most stable organization is the lowest possible energy, called the ground state. • 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. Electronic Structure of Atoms © 2015 Pearson Education, 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. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.” This means that, for a set of orbitals in the same sublevel, there must be one electron in each orbital before pairing and the electrons have the same spin, as much as possible. © 2015 Pearson Education, Inc. Electronic Structure of Atoms Condensed Electron Configurations • Elements in the same group of the periodic table have the same number of electrons in the outer most shell. These are the valence electrons. • The filled inner shell electrons are called core electrons. These include completely filled d or f sublevels. • We write a shortened version of an electron configuration using brackets around a noble gas symbol and listing only valence electrons. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Periodic Table • We fill orbitals in increasing order of energy. • Different blocks on the periodic table correspond to different types of orbitals: s = blue, p = pink (s and p are representative elements); d = orange (transition elements); f = tan (lanthanides and actinides, or inner transition elements) Electronic Structure of Atoms © 2015 Pearson Education, Inc. Some Anomalies Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. Electronic Structure of Atoms © 2015 Pearson Education, Inc. Chromium as an Anomaly • For instance, the electron configuration for chromium is [Ar] 4s1 3d5 rather than the expected [Ar] 4s2 3d4. • This occurs because the 4s and 3d orbitals are very close in energy. • These anomalies occur in f-block atoms Electronic with f and d orbitals, as well. Structure of Atoms © 2015 Pearson Education, Inc.