Chemistry: The Central Science - Chapter 6 - Electronic Structure of Atoms - PDF

Chemistry: The Central Science Fifteenth Edition Chapter 6 Electronic Structure of Atoms Copyright © 2023 Pearson Education, Inc. All Rights Reserv...

Chemistry: The Central Science Fifteenth Edition Chapter 6 Electronic Structure of Atoms Copyright © 2023 Pearson Education, Inc. All Rights Reserved 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. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.1 The Wave Nature of Light (1 of 2) To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. Electromagnetic radiation moves as waves through space at the speed of light. The distance between corresponding points on adjacent waves is the wavelength  . Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.1 The Wave Nature of Light (2 of 2) The number of waves passing a given point per unit of time is the frequency (ν). For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. The wave in (a) has double the wavelength of the wave in (b). The wave in (a) has half the frequency of the wave in (b). Copyright © 2023 Pearson Education, Inc. All Rights Reserved Electromagnetic Radiation (1 of 2) All electromagnetic radiation travels at the same velocity: The speed of light, c, is 3.00  108 m/s. Wavelength and frequency are related using c v Copyright © 2023 Pearson Education, Inc. All Rights Reserved Electromagnetic Radiation (2 of 2) Table 6.1 Common Wavelength Units for Electromagnetic Radiation Unit Symbol Length (m) Type of Radiation Angstrom Å letter A with small circular dot above 10  10 10 to the negative tenth power X ray Nanometer nm 10  9 10 to the negative ninth power Ultraviolet, visible Micrometer μm mu m 10  6 10 to the negative sixth power Infrared Millimeter mm 10  3 10 to the negative third power Microwave Centimeter cm 10  2 10 to the negative second power Microwave Meter m 1 Television, radio Kilometer km 1000 Radio There are many types of electromagnetic radiation. They have different wavelengths and energies from each other. The typical wavelength unit used vary based on the lengths. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.2 Quantized Energy and Photons Three observed properties associated with how atoms interact with electromagnetic radiation cannot be explained by waves: 1) The emission of light from hot objects (blackbody radiation) 2) The emission of electrons from metal surfaces on which light is shone (the photoelectric effect) 3) Emission of light from electronically excited gas atoms (emission spectra) Copyright © 2023 Pearson Education, Inc. All Rights Reserved Black Body Radiation An object glows when heated. The wave nature of light does not explain how an object can glow when its temperature increases. Classical physics predicted emission of UV, X-rays, and gamma rays. They were not observed. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Quanta Max Planck explained energy by assuming that energy comes in packets called quanta (singular: quantum). Think of stairs (quanta) versus a ramp (continuous). Copyright © 2023 Pearson Education, Inc. All Rights Reserved 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 hv where h is Planck’s constant, 6.626  10  34 J s. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Atomic Emission of Gas Another mystery in the early twentieth century involved the emission spectra observed from energy emitted by atoms and molecules. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.3 Line Spectra and the Bohr Model For atoms and molecules, one does not observe a continuous spectrum (the “rainbow”), as one gets from a white light source passed through a prism. Only a line spectrum of discrete wavelengths is observed. Each element has a unique line spectrum. Copyright © 2023 Pearson Education, Inc. All Rights Reserved The Hydrogen Spectrum Johann Balmer (1885) discovered a simple formula relating the four emission lines to integers. Johannes Rydberg advanced this formula. (RH is called the Rydberg constant.) 1  1 1  RH  2  2    n1 n2  Neils Bohr explained why this mathematical relationship works. Copyright © 2023 Pearson Education, Inc. All Rights Reserved The Bohr Model (1 of 3) Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 1) Only orbits of certain radii, corresponding to specific energies, are permitted for the electron in a hydrogen atom. Copyright © 2023 Pearson Education, Inc. All Rights Reserved The Bohr Model (2 of 3) 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 energy state to another. This energy is emitter of absorbed as a photon that has energy E h. Copyright © 2023 Pearson Education, Inc. All Rights Reserved The Bohr Model (3 of 3) Electrons in the lowest energy state are in the ground state, n = 1. Any energy higher is called an excited state, , n > 1. Since each orbit has a specific value compared to RH , transitions from one energy level to another can be calculated:  1 1  E Efi  E  2.18 10  18 J 2  2   nfi n  Copyright © 2023 Pearson Education, Inc. All Rights Reserved Energy State Values What do the values mean using the Bohr Model? A positive E means energy is absorbed. A photon is absorbed in this instance. This happens if nfi  n. A negative E means energy is released. A photon is emitted in this instance. This happens if nfi  n. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Limitations of the Bohr Model This model only works for hydrogen (one electron). 1. Classical physics would result in an electron falling into the positively charged nucleus. Bohr simply assumed it would not. 2. Electrons have wave-like properties that must be accommodated. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 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, which are described by quantum numbers. 2) Energy is involved in the transition of an electron from one level to another. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.4 The Wave Behavior 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: h The wave nature of  light is used to produce mv this electron micrograph. Copyright © 2023 Pearson Education, Inc. All Rights Reserved The Uncertainty Principle Heisenberg proposed the dual nature of matter (particle and wave) placed a limitation on how precisely we can know both momentum and position. He showed that the more precisely the momentum of a particle is known, the less precisely its position is known: h ( x )( mv )  4 Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.5 Quantum Mechanics and Atomic Orbitals 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. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Atomic Orbitals The solution of Schrödinger’s wave equation for hydrogen yields wave functions for the electron. The square of the wave function gives the electron density, or probability of where an electron is likely to be at any given time. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Orbitals and 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: n, l, ml Copyright © 2023 Pearson Education, Inc. All Rights Reserved Principal Quantum Number (n) The principal quantum number, n, describes the energy level on which the orbital resides. They are positive integral values 1, 2, 3,… They correspond to the values in the Bohr model. As n increases, the orbitals become larger, and the electron spends more time farther away from the nucleus. As n increases the electron also has a higher energy and is less tightly bound to the nucleus. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 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. Examples: If n 1, I 0 If n 2, I 0, 1 Letter also designate the different values of l. This defines the shape of the orbitals. Value of l 0 1 2 3 Letter used s p d f Copyright © 2023 Pearson Education, Inc. All Rights Reserved Magnetic Quantum Number (ml ) left parenthesis m sub l right parenthesis The magnetic quantum number describes the three- dimensional orientation of the orbital. Allowed values of m/ are integers ranging from  l to l including 0:  l ml l For any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, and so forth. – i.e. for s (I 0), mI 0 – i.e. for p (I 1), mI  1, 0, 1 – i.e. for d (I 2), mI  2,  1, 0, 1, 2 Copyright © 2023 Pearson Education, Inc. All Rights Reserved Quantum Numbers Summary Orbitals with the same value of n form an electron shell. Different orbital types within a shell are subshells. Table 6.2 Relationship among Values of n, l, and ml through n 4 Possible Subshell Number of Orbitals Total Number of n Values of l Designation Possible Values of m m sub l in Subshell Orbitals in Shell l 1 0 1s 0 1 1 2 0 2s 0 1 Blank 2 1 2p 1, 0, negative 1 3 4 1, 0,  1 3 0 3s 0 1 Blank 3 1 3p 1, 0, negative 1 3 Blank 3 2 3d 1, 0,  1 2, 1, 0, negative 1, negative 2 5 9 4 0 4s 2, 0 1, 0,  1,  2 1 Blank 4 1 4p 1, 0, negative 1 3 Blank 4 2 4d 1, 0,  1 2, 1, 0, negative 1, negative 2 5 Blank 4 3 4f 2, 1, 0,  1,  2 3, 2, 1, 0, negative 1, negative 2, negative 3 7 16 3, 2, 1, 0,  1,  2,  3 Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.6 Representation of Orbitals: s (1 of 2) 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. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.6 Representation of Orbitals: s (2 of 2) 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. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Representation of Orbitals: p The value of l for p orbitals is 1. They have two lobes with a node between them. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Representation of Orbitals: d 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. Copyright © 2023 Pearson Education, Inc. All Rights Reserved f Orbitals Very complicated shapes (not shown in text) Seven equivalent orbitals in a sublevel l=3 Copyright © 2023 Pearson Education, Inc. All Rights Reserved Hydrogen Atom Orbital Energies For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. Chemists call them degenerate orbitals. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.7 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 in energy than 3d.) Copyright © 2023 Pearson Education, Inc. All Rights Reserved Spin Quantum Number, ms m sub s 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 1 1 two allowed values,  and  2 2 Copyright © 2023 Pearson Education, Inc. All Rights Reserved Pauli Exclusion Principle No two electrons in the same atom can have the same set of four quantum numbers. Therefore, no two electrons in the same atom can have the exact same energy. This means that every electron in an atom must differ by at least one of the four quantum number values: n, I, ml , and ms. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.8 Electron Configurations (1 of 3) 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, here n = 4: 4 p5 Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.8 Electron Configurations (2 of 3) 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, here p: 4p 5 Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.8 Electron Configurations (3 of 3) 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, here there are 5 p electrons: 4p5 Copyright © 2023 Pearson Education, Inc. All Rights Reserved 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. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Hund’s Rule “When filling degenerate orbitals the lowest energy is attained when the number of electrons having the same spin is maximized.” Table 6.3 Electron Configurations of Several Lighter Elements Element Total Electrons Orbital Diagram Electron Configuration blank blank 1s 2s 2p 3s blank Li 3 The first element has the following orbital diagrams: 1 s has two half-headed arrows in which one is facing up and another is facing down. 2 s has one half arrow in which one is facing up. 2 p and 3 s are blank. 1s 2 2s1 1s 22s 1 Be 4 The second element has the following orbital diagrams: 1 s has two half-headed arrows in which one is facing up and another is facing down. 2 s has one half arrow in which one is facing up and another is facing down. 2 p and 3 s are blank. 1s 2 2s 2 1s 22s 2 B 5 The third element has the following orbital diagrams: 1 s has two half-headed arrows in which one is facing up and another is facing down. 2 s has one half arrow in which one is facing up and another is facing down. 2 p has a half arrow facing up in the first box. 3 s is blank. 1s 2 2s 2 2 p1 1s 22s 22p1 C 6 The fourth element has the following orbital diagrams: 1 s has two half-headed arrows in which one is facing up and another is facing down. 2 s has one half arrow in which one is facing up and another is facing down. 2 p has a half arrow facing up in the first box and has another half arrow facing up in the second box. 3 s is blank. 1s 2 2s 2 2 p 2 1s 22s 22p2 N 7 The fifth element has the following orbital diagrams: 1 s has two half-headed arrows in which one is facing up and another is facing down. 2 s has one half arrow in which one is facing up and another is facing down. 2 p has a half arrow facing up all of the boxes. 3 s is blank. 1s 2 2s 2 2 p3 1s 22s 22p3 Ne 10 The sixth element has the following orbital diagrams: 1 s has two half-headed arrows in which one is facing up and another is facing down. 2 s has one half arrow in which one is facing up and another is facing down. 2 p has two half-headed arrows, one facing up and one facing down, in all of the boxes. 3 s is blank. 1s 2 2s 2 2 p 6 1s 22s 22p6 Na 11 The seventh element has the following orbital diagrams: 1 s has two half-headed arrows in which one is facing up and another is facing down. 2 s has one half arrow in which one is facing up and another is facing down. 2 p has two half-headed arrows, one facing up and one facing down, in all of the boxes. 3 s has one electron facing up. 1s 2 2s 2 2 p 6 3s1 1s 22s 22p63s 1 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. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 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. They are noble gases. Always include completely filled d or f sublevels. We write a shortened version of an electron configuration using brackets around the core (noble gas symbol) and listing only valence electrons. – He is 1s2. – Li is 1s2 2 s1. We write [He]2s1. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Transition Metals Argon (atomic number 18) ends period 3. Its electron configuration is 1s 2 2s 2 2 p 6 3s 2 3 p 6. Potassium (atomic number 19) might be expected to have electrons in 3d. But 4s fills next. Transition metals follow the filling of 4s by filling 3d in the fourth period. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Lanthanides and Actinides The elements which fill the f orbitals have special names as a portion of a period, not as a group. The lanthanide elements (atomic numbers 57 to 70) have electrons entering the 4f sublevel. The actinide elements (including Uranium, at. no. 92, and Plutonium, at. no. 94) have electrons entering the 5f sublevel. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 6.9 Electron Configurations and the Periodic Table Orbitals fill 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) The s and p blocks are called the main-group elements. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Use the Periodic Table and to Write the Electron Configuration The periodic table is followed directly when determining the electron configuration for Most elements. For the element selenium, Se : [Ar] 4s 2 3d10 4p 4 Copyright © 2023 Pearson Education, Inc. All Rights Reserved Some Anomalies Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. Copyright © 2023 Pearson Education, Inc. All Rights Reserved 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 with f and d orbitals, as well. Copyright © 2023 Pearson Education, Inc. All Rights Reserved Copyright This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. Copyright © 2023 Pearson Education, Inc. All Rights Reserved