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Chemistry Third Edition Julia Burdge Lecture PowerPoints Chapter 6 Quantum Theory and the Electronic Structure of Atoms Copyright © 2012, The McGraw-Hill Compaies, Inc. Permission required for reproduction or display. CHAPTER 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6 Quantum Theory and the Electronic Structure of Atoms The Nature of Light Quantum Theory Bohr’s Theory of the Hydrogen Atom Wave Properties of Matter Quantum Mechanics Quantum Numbers Atomic Orbitals Electron Configuration Electron Configurations and the Periodic Table 2 6.1 The Nature of Light Topics Properties of Waves The Electromagnetic Spectrum The Double-Slit Experiment 3 6.1 The Nature of Light Properties of Waves When we say “light,” we generally mean visible light, which is the light we can detect with our eyes. Visible light, however, is only a small part of the continuum of radiation that comprises the electromagnetic spectrum. 4 6.1 The Nature of Light Properties of Waves Wavelength (lambda) is the distance between identical points on successive waves (e.g., successive peaks or successive troughs). 5 6.1 The Nature of Light Properties of Waves The frequency (nu) is the number of waves that pass through a particular point in 1 second. 6 6.1 The Nature of Light Properties of Waves Amplitude is the vertical distance from the midline of a wave to the top of the peak or the bottom of the trough. 7 6.1 The Nature of Light Properties of Waves The speed of light through a vacuum, c, is c = 2.99792458 × 108 m/s. The speed, wavelength, and frequency of a wave are related by the equation where and are expressed in meters (m) and reciprocal seconds (s–1), respectively. 8 SAMPLE PROBLEM 6.1 One type of laser used in the treatment of vascular skin lesions is a neodymium-doped yttrium aluminum garnet or Nd:YAG laser. The wavelength commonly used in these treatments is 532 nm. What is the frequency of this radiation? Setup Solving for frequency gives = c/. 9 SAMPLE PROBLEM 6.1 Solution 10 6.1 The Nature of Light Properties of Waves © Jim Wehtje/Getty Images 11 6.1 The Nature of Light The Electromagnetic Spectrum An electromagnetic wave has an electric field component and a magnetic field component. These two components have the same wavelength and frequency, and hence the same speed, but they travel in mutually perpendicular planes. 12 6.1 The Nature of Light The Double-Slit Experiment 13 6.2 Quantum Theory Topics Quantization of Energy Photons and the Photoelectric Effect 14 6.2 Quantum Theory Quantization of Energy When a solid is heated, it emits electromagnetic radiation, known as blackbody radiation, over a wide range of wavelengths. Attempts to model blackbody radiation in terms of established wave theory and thermodynamic laws were only partially successful. Planck developed a successful model by proposing that radiant energy could only be emitted or absorbed in discrete quantities, like small packages or bundles. 15 6.2 Quantum Theory Quantization of Energy Planck gave the name quantum to the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation. The energy E of a single quantum of energy is given by where h is called Planck’s constant and is the frequency of the radiation. The value of Planck’s constant is 6.63 × 10–34 J·s. 16 SAMPLE PROBLEM 6.2 How much more energy per photon is there in green light of wavelength 532 nm than in red light of wavelength 635 nm? Setup 17 SAMPLE PROBLEM 6.2 Solution Following the same procedure, the energy of a photon of wavelength 635 nm is 3.13 × 10–19 J. 18 SAMPLE PROBLEM 6.2 Solution The difference between them is (3.74 × 10–19 J) – (3.13 × 10–19 J) = 6.1 × 10–20 J. Therefore, a photon of green light ( = 532 nm) has 6.1 × 10–20 J more energy than a photon of red light ( = 635 nm). 19 6.2 Quantum Theory Photons and the Photoelectric Effect In the photoelectric effect, electrons are ejected from the surface of a metal exposed to light of at least a certain minimum frequency, called the threshold frequency . The photoelectric effect could not be explained by the wave theory of light, which associated the energy of light with its intensity. 20 6.2 Quantum Theory Photons and the Photoelectric Effect Einstein, however, made an extraordinary assumption. He suggested that a beam of light is really a stream of particles. These particles of light are now called photons. Using Planck’s quantum theory of radiation as a starting point, Einstein deduced that each photon must possess energy E given by the equation where h is Planck’s constant and is the frequency of the light. 21 6.2 Quantum Theory Photons and the Photoelectric Effect If the frequency of the photons is such that h exactly equals the energy that binds the electrons in the metal, then the light will have just enough energy to knock the electrons loose. If we use light of a higher frequency, then not only will the electrons be knocked loose, but they will also acquire some kinetic energy. This situation is summarized by the equation where KE is the kinetic energy of the ejected electron and W is the binding energy of the electron in the metal. 22 SAMPLE PROBLEM 6.3 Calculate the energy (in joules) of (a) a photon with a wavelength of 5.00 × 104 nm (infrared region) and (b) a photon with a wavelength of 52 nm (ultraviolet region). (c) Calculate the kinetic energy of an electron ejected by the photon in part (b) from a metal with a binding energy of 3.7 eV. 23 SAMPLE PROBLEM 6.3 Setup (a) (b) (c) 24 SAMPLE PROBLEM 6.3 Solution (b) Following the same procedure as in part (a), the energy of a photon of wavelength 52 nm is 3.8 × 10–18 J. 25 6.3 Bohr’s Theory of the Hydrogen Atom Topics Atomic Line Spectra The Line Spectrum of Hydrogen 26 6.3 Bohr’s Theory of the Hydrogen Atom Atomic Line Spectra The emission spectra of atoms in the gas phase do not show a continuous spread of wavelengths from red to violet; rather, the atoms produce bright lines in distinct parts of the visible spectrum. These line spectra are the emission of light only at specific wavelengths. 27 6.3 Bohr’s Theory of the Hydrogen Atom Atomic Line Spectra 28 6.3 Bohr’s Theory of the Hydrogen Atom 29 6.3 Bohr’s Theory of the Hydrogen Atom Atomic Line Spectra Johannes Rydberg developed an equation that could calculate all the wavelengths of hydrogen’s spectral lines: In this equation, now known as the Rydberg equation, is the wavelength of a line in the spectrum; R∞ is the Rydberg constant (1.09737316 × 107 m–1); and n1 and n2 are positive integers, where n2 > n1. 30 6.3 Bohr’s Theory of the Hydrogen Atom The Line Spectrum of Hydrogen According to the laws of classical physics, an electron moving in an orbit of a hydrogen atom would radiate away energy in the form of electromagnetic waves. Thus, such an electron would quickly spiral into the nucleus and annihilate itself with the proton. 31 6.3 Bohr’s Theory of the Hydrogen Atom The Line Spectrum of Hydrogen Bohr postulated that the electron in atomic hydrogen is allowed to occupy only certain orbits of specific energies. In other words, the energies of the electron are quantized. An electron in any of the allowed orbits will not radiate energy and therefore will not spiral into the nucleus. 32 6.3 Bohr’s Theory of the Hydrogen Atom The Line Spectrum of Hydrogen Bohr showed that the energies that the electron in the hydrogen atom can possess are given by where n is an integer with values n = 1, 2, 3, and so on. The most negative value, then, is reached when n = 1, which corresponds to the most stable energy state. We call this the ground state, the lowest energy state of an atom. 33 6.3 Bohr’s Theory of the Hydrogen Atom The Line Spectrum of Hydrogen Each energy state in which n > 1 is called an excited state. The radius of each circular orbit in Bohr’s model depends on n2. Thus, as n increases from 1 to 2 to 3, the orbit radius increases very rapidly. Radiant energy absorbed by the atom causes the electron to move from the ground state (n = 1) to an excited state (n > 1). state. 34 6.3 Bohr’s Theory of the Hydrogen Atom The Line Spectrum of Hydrogen Conversely, radiant energy (in the form of a photon) is emitted when the electron moves from a higher-energy excited state to a lower-energy excited state or the ground state. 35 6.3 Bohr’s Theory of the Hydrogen Atom The Line Spectrum of Hydrogen 36 6.3 Bohr’s Theory of the Hydrogen Atom The Line Spectrum of Hydrogen 37 6.3 Bohr’s Theory of the Hydrogen Atom The Line Spectrum of Hydrogen 38 6.3 Bohr’s Theory of the Hydrogen Atom 39 SAMPLE PROBLEM 6.4 Calculate the wavelength (in nm) of the photon emitted when an electron transitions from the n = 4 state to the n = 2 state in a hydrogen atom . Setup According to the problem, the transition is from n = 4 to n = 2, so ni = 4 and nf = 2. The required constants are h = 6.63 × 10–34 J · s and c = 3.00 × 108 m/s. 40 SAMPLE PROBLEM 6.4 Solution 41 6.4 Wave Properties of Matter Topics The de Broglie Hypothesis Diffraction of Electrons 42 6.4 Wave Properties of Matter The de Broglie Hypothesis The waves generated by plucking a guitar string are standing or stationary waves because they do not travel along the string. Some points on the string, called nodes, do not move at all; that is, the amplitude of the wave at these points is zero. There is a node at each end, and there may be one or more nodes between the ends. The greater the frequency of vibration, the shorter the wavelength of the standing wave and the greater the number of nodes. 43 6.4 Wave Properties of Matter The de Broglie Hypothesis 44 6.4 Wave Properties of Matter The de Broglie Hypothesis According to de Broglie, an electron in an atom behaves like a standing wave. However, only certain wavelengths are possible or allowed. The relationship between the circumference of an allowed orbit (2r) and the wavelength () of the electron is given by 45 6.4 Wave Properties of Matter The de Broglie Hypothesis Because n is an integer, r can have only certain values (integral multiples of ) as n increases from 1 to 2 to 3 and so on. And, because the energy of the electron depends on the size of the orbit (or the value of r), the energy can have only certain values, too. Thus, the energy of the electron in a hydrogen atom, if it behaves like a standing wave, must be quantized. 46 6.4 Wave Properties of Matter The de Broglie Hypothesis De Broglie’s reasoning led to the conclusion that waves can behave like particles and particles can exhibit wavelike properties. De Broglie deduced that the particle and wave properties are related by the following expression: where , m, and u are the wavelength associated with a moving particle, its mass, and its velocity, respectively. 47 6.4 Wave Properties of Matter The de Broglie Hypothesis A wavelength calculated using is usually referred to specifically as a de Broglie wavelength. Likewise, we will refer to a mass calculated using the equation as a de Broglie mass. 48 SAMPLE PROBLEM 6.5 Calculate the de Broglie wavelength of the “particle” in the following two cases: (a) a 25-g bullet traveling at 612 m/s, and (b) an electron (m = 9.109 × 10–31 kg) moving at 63.0 m/s. Setup Planck’s constant, h, is 6.63 × 10–34 J · s or, for the purpose of making the unit cancellation obvious, 6.63 × 10–34 kg · m2/s. Remember that 1 J = 1 kg · m2/s2. Solution 49 SAMPLE PROBLEM 6.5 Solution 50 6.4 Wave Properties of Matter Diffraction of Electrons Experiments demonstrate that electrons do indeed possess wavelike properties. By directing a beam of electrons (which are most definitely particles) through a thin piece of gold foil, Thomson obtained a set of concentric rings on a screen, similar to the diffraction pattern observed when X rays (which are most definitely waves) were used. Erwin Schrodinger, Wave Mechanical Model of the Atom. 1926 51 6.5 Quantum Mechanics Topics The Uncertainty Principle The Schrödinger Equation The Quantum Mechanical Description of the Hydrogen Atom 52 6.5 Quantum Mechanics The Uncertainty Principle To describe the problem of trying to locate a subatomic particle that behaves like a wave, Werner Heisenberg formulated what is now known as the Heisenberg uncertainty principle: It is impossible to know simultaneously both the momentum p and the position x of a particle with certainty. Stated mathematically, 53 6.5 Quantum Mechanics The Uncertainty Principle For a particle of mass m, where x and u are the uncertainties in measuring the position and velocity of the particle, respectively. Thus, making measurement of the velocity of a particle more precise means that the position must become correspondingly less precise. Similarly, if the position of the particle is known more precisely, its velocity measurement must become less precise. 54 SAMPLE PROBLEM 6.6 An electron in a hydrogen atom is known to have a velocity of 5 × 106 m/s 1 percent. Using the uncertainty principle, calculate the minimum uncertainty in the position of the electron and, given that the diameter of the hydrogen atom is less than 1 angstrom (Å), comment on the magnitude of this uncertainty compared to the size of the atom. Setup The mass of an electron is 9.11 × 10–31 kg. Planck’s constant, h, is 6.63 × 10–34 kg · m2/s. 55 SAMPLE PROBLEM 6.6 Solution The minimum uncertainty in the position x is 1 × 10–9 m = 10 Å. The uncertainty in the electron’s position is 10 times larger than the atom! 56 6.5 Quantum Mechanics The Schrödinger Equation Erwin Schrödinger, using a complex mathematical technique, formulated an equation that describes the behavior and energies of submicroscopic particles in general. The Schrödinger equation requires advanced calculus to solve, and we will not discuss it here. The equation, however, incorporates both particle behavior, in terms of mass m, and wave behavior, in terms of a wave function (psi), which depends on the location in space of the system (such as an electron in an atom). 57 6.5 Quantum Mechanics The Schrödinger Equation The wave function itself has no direct physical meaning. However, the probability of finding the electron in a certain region in space is proportional to the square of the wave function, 2. The idea of relating 2 to probability stemmed from a wave theory analogy. 58 6.5 Quantum Mechanics The Quantum Mechanical Description of the Hydrogen Atom The Schrödinger equation specifies the possible energy states the electron can occupy in a hydrogen atom and identifies the corresponding wave functions (). These energy states and wave functions are characterized by a set of quantum numbers (to be discussed shortly), with which we can construct a comprehensive model of the hydrogen atom. 59 6.5 Quantum Mechanics The Quantum Mechanical Description of the Hydrogen Atom The square of the wave function, 2, defines the distribution of electron density in three-dimensional space around the nucleus. Regions of high electron density represent a high probability of locating the electron. 60 6.5 Quantum Mechanics The Quantum Mechanical Description of the Hydrogen Atom To distinguish the quantum mechanical description of an atom from Bohr’s model, we speak of an atomic orbital, rather than an orbit. An atomic orbital can be thought of as the wave function of an electron in an atom. When we say that an electron is in a certain orbital, we mean that the distribution of the electron density or the probability of locating the electron in space is described by the square of the wave function associated with that orbital. 61 6.5 Quantum Mechanics The Quantum Mechanical Description of the Hydrogen Atom An atomic orbital, therefore, has a characteristic energy, as well as a characteristic distribution of electron density. 62 6.6 Quantum Numbers Topics Principal Quantum Number (n) Angular Momentum Quantum Number (l) Magnetic Quantum Number (ml) Electron Spin Quantum Number (ms) 63 6.6 Quantum Numbers Principal Quantum Number (n) In quantum mechanics, three quantum numbers are required to describe the distribution of electron density in an atom. These numbers are derived from the mathematical solution of Schrödinger’s equation for the hydrogen atom. 64 6.6 Quantum Numbers Principal Quantum Number (n) The principal quantum number (n) designates the size of the orbital. The larger n is, the greater the average distance of an electron in the orbital from the nucleus and therefore the larger the orbital. n = 1, 2, 3, … 65 6.6 Quantum Numbers Angular Momentum Quantum Number (l) The angular momentum quantum number (l) describes the shape of the atomic orbital. The values of l are integers that depend on the value of the principal quantum number, n. For a given value of n, the possible values of l range from 0 to n – 1. 66 6.6 Quantum Numbers Angular Momentum Quantum Number (l) A collection of orbitals with the same value of n is frequently called a shell. One or more orbitals with the same n and l values are referred to as a subshell. For example, the shell designated by n = 2 is composed of two subshells: l = 0 and l = 1 (the allowed values of l for n = 2). These subshells are called the 2s and 2p subshells where 2 denotes the value of n, and s and p denote the values of l. 67 6.6 Quantum Numbers Magnetic Quantum Number (ml) The magnetic quantum number (ml ) describes the orientation of the orbital in space. Within a subshell, the value of ml depends on the value of l. For a certain value of l, there are (2l + 1) integral values of ml as follows: –l, …, 0 , …, +l 68 6.6 Quantum Numbers 69 6.6 Quantum Numbers Magnetic Quantum Number (ml) 70 SAMPLE PROBLEM 6.7 What are the possible values for the magnetic quantum number (ml) when the principal quantum number (n) is 3 and the angular momentum quantum number (l) is 1? Setup The possible values of ml are –l, . . . , 0, . . . , +l. Solution The possible values of ml are –1, 0, and +1. 71 6.6 Quantum Numbers Electron Spin Quantum Number (ms) Whereas three quantum numbers are sufficient to describe an atomic orbital, an additional quantum number becomes necessary to describe an electron that occupies the orbital. Electrons possess a magnetic field, as if they were spinning. 72 6.6 Quantum Numbers Electron Spin Quantum Number (ms) To specify the electron’s spin, we use the electron spin quantum number (ms). Because there are two possible directions of spin, opposite each other, ms has two possible values: +1/2 and –1/2. Two electrons in the same orbital with opposite spins are referred to as “paired.” 73 6.6 Quantum Numbers Electron Spin Quantum Number (ms) To summarize, we can designate an orbital in an atom with a set of three quantum numbers. These three quantum numbers indicate the size (n), shape (l), and orientation (ml) of the orbital. A fourth quantum number (ms) is necessary to designate the spin of an electron in the orbital. 74 6.7 Atomic Orbitals Topics s Orbitals p Orbitals d Orbitals and Other Higher-Energy Orbitals Energies of Orbitals 75 6.7 Atomic Orbitals s Orbitals For any value of the principal quantum number (n), the value 0 is possible for the angular momentum quantum number (l), corresponding to an s subshell. Furthermore, when l = 0, the magnetic quantum number (ml) has only one possible value, 0, corresponding to an s orbital. Therefore, there is an s subshell in every shell, and each s subshell contains just one orbital, an s orbital. 76 6.7 Atomic Orbitals 77 6.7 Atomic Orbitals s Orbitals All s orbitals are spherical in shape but differ in size, which increases as the principal quantum number increases. 78 6.7 Atomic Orbitals p Orbitals When the principal quantum number (n) is 2 or greater, the value 1 is possible for the angular momentum quantum number (l), corresponding to a p subshell. And, when l = 1, the magnetic quantum number (ml) has three possible values: –1, 0, and +1, each corresponding to a different p orbital. 79 6.7 Atomic Orbitals p Orbitals Therefore, there is a p subshell in every shell for which n 2, and each p subshell contains three p orbitals. These three p orbitals are labeled px , py , and pz . 80 6.7 Atomic Orbitals p Orbitals These three p orbitals are identical in size, shape, and energy; they differ from one another only in orientation. Like s orbitals, p orbitals increase in size from 2p to 3p to 4p orbital and so on. 81 6.7 Atomic Orbitals d Orbitals and Other Higher-Energy Orbitals When the principal quantum number (n) is 3 or greater, the value 2 is possible for the angular momentum quantum number (l), corresponding to a d subshell. When l = 2, the magnetic quantum number (ml) has five possible values, –2, –1, 0, +1, and +2, each corresponding to a different d orbital. 82 6.7 Atomic Orbitals d Orbitals and Other Higher-Energy Orbitals 83 6.7 Atomic Orbitals d Orbitals and Other Higher-Energy Orbitals All the 3d orbitals in an atom are identical in energy and are labeled with subscripts denoting their orientation with respect to the x, y, and z axes and to the planes defined by them. The d orbitals that have higher principal quantum numbers (4d, 5d, etc.) have shapes similar to those shown for the 3d orbitals . 84 6.7 Atomic Orbitals d Orbitals and Other Higher-Energy Orbitals The f orbitals are important when accounting for the behavior of elements with atomic numbers greater than 57, but their shapes are difficult to represent. In general chemistry we will not concern ourselves with the shapes of orbitals having l values greater than 2. 85 SAMPLE PROBLEM 6.8 List the values of n, l, and ml for each of the orbitals in a 4d subshell. Strategy Consider the significance of the number and the letter in the 4d designation and determine the values of n and l. There are multiple possible values for ml, which will have to be deduced from the value of l. 86 SAMPLE PROBLEM 6.8 Setup The integer at the beginning of an orbital designation is the principal quantum number (n). The letter in an orbital designation gives the value of the angular momentum quantum number (l). The magnetic quantum number (ml) can have integral values of –l, . . . , 0, . . . , +l. 87 SAMPLE PROBLEM 6.8 Solution The values of n and l are 4 and 2, respectively, so the possible values of ml are –2, –1, 0, +1, and +2. 88 6.7 Atomic Orbitals Energies of Orbitals 89 6.7 Atomic Orbitals Energies of Orbitals 90 6.8 Electron Configuration Topics Energies of Atomic Orbitals in Many-Electron Systems The Pauli Exclusion Principle The Aufbau Principle Hund’s Rule General Rules for Writing Electron Configurations 91 6.8 Electron Configuration Energies of Atomic Orbitals in Many-Electron Systems The hydrogen atom is a particularly simple system because it contains only one electron. The electron may reside in the 1s orbital (the ground state), or it may be found in some higher-energy orbital (an excited state). With many-electron systems, we need to know the groundstate electron configuration—that is, how the electrons are distributed in the various atomic orbitals. 92 6.8 Electron Configuration Energies of Atomic Orbitals in Many-Electron Systems To do this, we need to know the relative energies of atomic orbitals in a many-electron system, which differ from those in a one-electron system such as hydrogen. In many-electron atoms, electrostatic interactions cause the energies of the orbitals in a shell to split. 93 6.8 Electron Configuration 94 6.8 Electron Configuration The Pauli Exclusion Principle According to the Pauli exclusion principle, no two electrons in the same atom can have the same four quantum numbers. If two electrons in an atom have the same n, l, and ml values (meaning that they occupy the same orbital), then they must have different values of ms; that is, one must have ms = –1/2 and the other must have ms = +1/2. 95 6.8 Electron Configuration The Pauli Exclusion Principle Because there are only two possible values for ms, and no two electrons in the same orbital may have the same value for ms, a maximum of two electrons may occupy an atomic orbital, and these two electrons must have opposite spins. Two electrons in the same orbital with opposite spins are said to have paired spins. 96 6.8 Electron Configuration The Pauli Exclusion Principle Orbital Notation and Orbital Diagrams 97 6.8 Electron Configuration The Aufbau Principle We can continue the process of writing electron configurations for elements based on the order of orbital energies and the Pauli exclusion principle. This process is based on the Aufbau principle, which makes it possible to “build” the periodic table of the elements and determine their electron configurations by steps. Each step involves adding one proton to the nucleus and one electron to the appropriate atomic orbital. 98 6.8 Electron Configuration The Aufbau Principle 1s22s22p1 99 6.8 Electron Configuration Hund’s Rule According to Hund’s rule, the most stable arrangement of electrons in orbitals of equal energy is the one in which the number of electrons with the same spin is maximized. 100 6.8 Electron Configuration Hund’s Rule 101 6.8 Electron Configuration General Rules for Writing Electron Configurations 1. Electrons will reside in the available orbitals of the lowest possible energy. 2. Each orbital can accommodate a maximum of two electrons. 3. Electrons will not pair in degenerate orbitals if an empty orbital is available. 4. Orbitals will fill in the order indicated in the following figure. 102 6.8 Electron Configuration 103 SAMPLE PROBLEM 6.9 Write the electron configuration and give the orbital diagram of a calcium (Ca) atom (Z = 20). Strategy Use the general rules given and the Aufbau principle to “build” the electron confi guration of a calcium atom and represent it with an orbital diagram. Setup Because Z = 20, we know that a Ca atom has 20 electrons. 104 SAMPLE PROBLEM 6.9 Solution 105 6.9 Electron Configurations and the Periodic Table Topics Electron Configurations and the Periodic Table 106 6.9 Electron Configurations and the Periodic Table Electron Configurations and the Periodic Table The electron configurations of all elements except hydrogen and helium can be represented using a noble gas core, which shows in brackets the electron configuration of the noble gas element that most recently precedes the element in question, followed by the electron configuration in the outermost occupied subshells. 107 6.9 Electron Configurations and the Periodic Table 108 6.9 Electron Configurations and the Periodic Table 109 6.9 Electron Configurations and the Periodic Table Electron Configurations and the Periodic Table Anomalies 110 6.9 Electron Configurations and the Periodic Table Electron Configurations and the Periodic Table Anomalies The reason for these anomalies is that a slightly greater stability is associated with the half-filled (3d5) and completely filled (3d10) subshells. 111 6.9 Electron Configurations and the Periodic Table Electron Configurations and the Periodic Table Anomalies There are several other anomalies as well in the transition metals, the lanthanides, and the actinides. 112 6.9 Electron Configurations and the Periodic Table Electron Configurations and the Periodic Table 113 SAMPLE PROBLEM 6.10 Write the electron configuration for an arsenic atom (Z = 33) in the ground state. Setup The noble gas core for As is [Ar], where Z = 18 for Ar. The order of filling beyond the noble gas core is 4s, 3d, and 4p. Fifteen electrons must go into these subshells because there are 33 – 18 = 15 electrons in As beyond its noble gas core. 114 SAMPLE PROBLEM 6.10 Solution 115