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Chapter 8 Modern Atomic Theory Setting the Stage – Emission of Light The beautiful color of fireworks comes from the particular elements used. The colors are characteristic of the elements and can be used to understand their properties. Malone and Dolter - Basic Concepts of Chemistry 9e 2 Setting a Goal – Part A The Emission Spectra of the Elements and Bohr’s Model You will understand historically how elemental emission spectra were used to determine the structure electrons adopt within an atom. For more details, see “Special Topics” Malone and Dolter - Basic Concepts of Chemistry 9e 3 Objectives for Section 8-1 8-1a Describe the relationships among the wavelengths of light, energy, and color. 8-1b Describe the relationship between emission spectra and the electronic structure of the hydrogen atom as explained by Bohr’s model. Malone and Dolter - Basic Concepts of Chemistry 9e 4 Two Atom-Sized Jokes Two Hydrogen atoms sit down at a bar. One says to the other "I think I've lost an electron." The other says "Are you sure?", and he replies, "Yeah, I'm positive." So a neutron walks into a bar, sits down and asks for a glass of soda. Finishing his drink, the neutron asks "How much?" The bartender says, "For you, no charge." Malone and Dolter - Basic Concepts of Chemistry 9e 5 8-1 The Emission Spectra of the Elements and Bohr’s Model The Nature of Light Electromagnetic energy Travels at 3.0 1010 cm/s White light is a continuous spectrum of light (all energies represented) and can be separated. Refer to Figure 8-1 in text. Malone and Dolter - Basic Concepts of Chemistry 9e 6 The Visible Spectrum Malone and Dolter - Basic Concepts of Chemistry 9e 7 Properties of Light Light has intensity, which is termed amplitude. Light is characterized by its wavelength, which is given the symbol (lambda). Wavelength is the distance between two adjacent peaks. Malone and Dolter - Basic Concepts of Chemistry 9e 8 Wavelength and Energy Wavelength and energy have an inverse relationship, as shown below. h is Planck’s constant (6.626 10-34 J·s) c is the speed of light E 1 hc E = Malone and Dolter - Basic Concepts of Chemistry 9e 9 Wavelength, frequency and velocity The velocity of propagated light waves in vacuum (c) = 2.998 x 108 m/s It is the product of the wavelength and wave frequency: c = n Malone and Dolter - Basic Concepts of Chemistry 9e 10 Period and Frequency The period (t) of the wave is the time taken for the wave to travel one complete wavelength. The frequency (n) is the reciprocal of the period (n = 1/t) Energy and frequency are directly proportional; E = hn (originally from Planck’s quantum theory) Malone and Dolter - Basic Concepts of Chemistry 9e 11 Visible Light Visible light comprises only a small fraction of the electromagnetic spectrum (400-800 nm). Ultraviolet and infrared light cannot be seen with the unaided eye, but are important. Malone and Dolter - Basic Concepts of Chemistry 9e 12 Energy Range of Light Infrared light is of lower energy than visible light. Ultraviolet light is of higher energy than visible light (some of the ultraviolet range is of high enough energy to damage living tissue). X-rays and gamma rays are even higher energy forms of light (there are special hazards associated with this type of radiation). Malone and Dolter - Basic Concepts of Chemistry 9e 13 Emission Spectra of Atoms When atoms are excited (like in a flame) they emit discrete wavelengths of light, not a continuum. These are called atomic emission (line) spectra Shown below is the visible light range at the top, the emission spectrum of Na in the middle and the emission spectrum of H at the bottom. Malone and Dolter - Basic Concepts of Chemistry 9e 14 Measuring the Emission Spectrum The H2 in the gas discharge tube is excited by electricity. The light produced is separated by the prism. Malone and Dolter - Basic Concepts of Chemistry 9e 15 Atomic Phenomena and Classical Physics Classical physics (Newtonian mechanics and Maxwell’s electromagnetism theory) could not explain: Emission line spectra The Rutherford (nuclear) model of the atom Black body radiation Photoelectric effect Electron diffraction Malone and Dolter - Basic Concepts of Chemistry 9e 16 A Model for the Electrons in the Atom A model is a description or analogy used to help visualize a phenomenon or entity. Bohr proposed a model that violated classical physics, but started a new way of looking at atomic and molecular structure. The central concept of this model is that the properties of atoms and electrons do not behave in a continuous fashion. Malone and Dolter - Basic Concepts of Chemistry 9e 17 The Bohr Atom Electrons revolve around the nucleus in certain stable orbits only. Each stable orbit is quantized the electron is a discrete distance from the nucleus the orbit has a discrete energy These orbits are referred to as energy levels. The energy levels are characterized by an integral number called the principle quantum number, n. Malone and Dolter - Basic Concepts of Chemistry 9e 18 The Bohr Atom (con’t.) n has discrete values of 1, 2, 3,… The quantum number n arose from Bohr’s idea of imposing quantization (from Planck’s Hypothesis, 1901) on the angular momentum of the electron. Otherwise Bohr’s description of the hydrogen atom uses classical physics. Light is absorbed (giving an absorption line) or emitted (an emission line) only when an electron changes its stable orbit (excitation or relaxation) – see next slide Malone and Dolter - Basic Concepts of Chemistry 9e 19 Balmer Emission Series of Hydrogen Explained by Bohr Theory Each energy level is associated with a particular Bohr orbit Malone and Dolter - Basic Concepts of Chemistry 9e 20 Quantized Energy Levels Quantized energy levels are like the steps of a staircase. An electron can have one energy or another, but not an energy in between (can you stand between two steps?) Malone and Dolter - Basic Concepts of Chemistry 9e 21 States of the Atom Ground state the lowest energy state Excited state all states that have higher energies atoms and molecules have many excited states but only one ground state Malone and Dolter - Basic Concepts of Chemistry 9e 22 Objectives for Section 8-2 8-2a Differentiate between a shell, a subshell, and an orbital. 8-2b Identify an s, p, or d-type orbital from its shape. Malone and Dolter - Basic Concepts of Chemistry 9e 23 8-2 Modern Atomic Theory: A Closer Look at Energy Levels •Bohr’s model of the hydrogen atom explained the emission spectra of hydrogen – a great success • However, even after several modifications, it was generally unsuccessful when applied to other atomic phenomena and failed totally to describe the helium atom Malone and Dolter - Basic Concepts of Chemistry 9e 24 Modern Atomic Theory - Wave Mechanics Modern atomic theory involves complex mathematical descriptions. It takes into account that atomic-sized things behave more like waves than particles. The Schrödinger equation for a hydrogen atom Malone and Dolter - Basic Concepts of Chemistry 9e 25 Wave Mechanics We treat electrons as waves, since we cannot precisely determine the location of the electrons. The idea was originally put forward by de Broglie: all matter has some wave character Schrödinger was the first person to apply de Broglie’s idea; he considered the electron in a hydrogen atom as a standing wave Electrons are said to be described by orbitals, which are regions in space where there is a significant probability of finding the electron. Malone and Dolter - Basic Concepts of Chemistry 9e 26 Extra Details Revealed Wave mechanics reveals that the energy levels (sometimes called shells) have sublevels. The sublevels are designated by letters: s, p, d, f The sublevels increase in energy as s<p<d<f Each sublevel has one or more orbitals. Malone and Dolter - Basic Concepts of Chemistry 9e 27 Some Heroes of Modern Atomic Theory E. Rutherford N. Bohr L. de Broglie W. Heisenberg Malone and Dolter - Basic Concepts of Chemistry 9e E. Schrödinger 28 Orbitals The orbital is best thought of as an electron cloud. The picture below is the density diagram for an s orbital. It indicates the probability of an electron being located in a particular location near the nucleus. Malone and Dolter - Basic Concepts of Chemistry 9e 29 Representing Orbitals We often represent orbitals as spherical volumes of probability (volume in which the electron is found 90% of the time). The orbitals of the s sublevel are shown below, for n = 1 and n = 2. 1s 2s Malone and Dolter - Basic Concepts of Chemistry 9e 30 p-Orbitals There are three orbitals in the p sublevel (starting at n = 2). One is aligned along each of the Cartesian axes around the nucleus. Orientation is indicated by subscript x, y or z. This is the set of 2p orbitals: Malone and Dolter - Basic Concepts of Chemistry 9e 31 d-Orbitals There are five orbitals in the d-sublevel, starting at n = 3. They are important to understanding the behavior of the transition metals and elements in period 3 and beyond. This is the set of 3d orbitals: Malone and Dolter - Basic Concepts of Chemistry 9e 32 Shell Designation The shell is indicated by the principle quantum number n. The subshell is indicated by the letter (s, p, d, f). The number of electrons in the subshell is indicated by a right superscript. For example, 4p3 (4th shell, p subshell, three electrons). Malone and Dolter - Basic Concepts of Chemistry 9e 33 Electronic Configurations The electrons in the atom are indicated by an electron configuration. We use only as many subshells and shells as are needed for the number of electrons. The number of available subshells depends on the shell that is being filled. n = 1 only has an s subshell n = 2 has s and p subshells n = 3 has s, p, and d subshells n = 4 has s, p, d, and f subshells Malone and Dolter - Basic Concepts of Chemistry 9e 34 The n = 3 Shell Malone and Dolter - Basic Concepts of Chemistry 9e 35 Dorm Room Analogy We can think of the levels as dorm rooms. A student will choose the dorm that is closest to the campus and a room on the lowest floor. Malone and Dolter - Basic Concepts of Chemistry 9e 36 Dorm Room Analogy, con’t The dorms correspond to the shells The floors correspond to the subshells Malone and Dolter - Basic Concepts of Chemistry 9e 37 Setting a Goal – Part B The Periodic Table and Electron Configuration You will have a detailed understanding of the structure of electrons in atoms, and how this affects that element’s properties. Malone and Dolter - Basic Concepts of Chemistry 9e 38 Objective for Section 8-3 Using the periodic table, write the outer electron configuration of a specific element. Malone and Dolter - Basic Concepts of Chemistry 9e 39 8-3 Electron Configurations of the Elements The Aufbau Principle The electrons are added to the atom beginning with the lowest energy level. As the sublevels and levels are filled, electrons are added to the next highest energy level. Each orbital can hold two electrons, so each sublevel can hold twice as many electrons as there are orbitals. Malone and Dolter - Basic Concepts of Chemistry 9e 40 The Aufbau Principle Electrons occupy the available orbitals in the subshells of lowest energy. The electronic configuration of an element is the assignment of all of the electrons of the atom into shells and subshells. Malone and Dolter - Basic Concepts of Chemistry 9e 41 Assignment of Electrons into Shells and Subshells Nomenclature or symbolism for electron configuration Malone and Dolter - Basic Concepts of Chemistry 9e 42 Ground States of the First Few Elements Using the Aufbau Principle, the electron configurations for the first 10 elements are: H He Li Be B C N O F Ne 1s1 1s2 1s22s1 1s22s2 1s22s22p1 1s22s22p2 1s22s22p3 1s22s22p4 1s22s22p5 1s22s22p6 Malone and Dolter - Basic Concepts of Chemistry 9e 43 Abbreviated Electron Configurations We develop a shorthand for the electron configuration by noting that the core is really the same as the electron configuration for the noble gas that occurs earlier in the periodic table. Example: for S (1s22s22p63s23p4), the core is 1s22s22p6 which is the same as the electron configuration for Ne. So the abbreviated form is [Ne]3s23p4 Malone and Dolter - Basic Concepts of Chemistry 9e 44 Electron Configuration Shorthand We note that the valence shell electron configuration has the same pattern for elements in the same group. All elements in the same column as oxygen or sulfur (group VIA) have the valence electron configuration [core]ns2np4. Malone and Dolter - Basic Concepts of Chemistry 9e 45 Periodic Nature of the Filling We find that at the end of a period, the pattern of electron filling repeats with higher values of n. F [He]2s22p5 Cl [Ne]3s23p5 Br [Core]4s24p5 The noble gas in parentheses indicates the inner electrons. Malone and Dolter - Basic Concepts of Chemistry 9e 46 Electronic Configurations The levels increase in energy. Within the levels, the sublevels also increase (recall s<p<d<f). Recall that the electrons go into the lowest orbital first (1s, then 2s, etc.). Malone and Dolter - Basic Concepts of Chemistry 9e 47 Shell, Subshell and Orbitals Malone and Dolter - Basic Concepts of Chemistry 9e 48 Core and Valence Shells Chemically, we find that the electrons in the shell with the highest value of n are the ones involved in chemical reactions. This shell is termed the valence shell. Electrons in shells with lower n values are chemically unreactive because they are of such low energy. These shells are grouped together as the core. Malone and Dolter - Basic Concepts of Chemistry 9e 49 Order of Filling of Atomic Orbitals The diagram opposite is a useful pictorial description of atomic orbital energy order Malone and Dolter - Basic Concepts of Chemistry 9e 50 Exceptions to the Filling Order They occur in atoms where the d or f orbitals are being filled. E.g. the ground state electron configuration of Cr (Z = 24) is [Ar]4s13d5, and not [Ar]4s23d4, as expected from the Aufbau Principle. Generally, it is not important or necessary to know them all. Malone and Dolter - Basic Concepts of Chemistry 9e 51 Representative Elements Representative elements have the general electron configuration [NG]nsxnpy (NG represents noble gas or core configuration). Each representative element has one more electron in the valence shell than the previous element. Malone and Dolter - Basic Concepts of Chemistry 9e 52 Representative Elements [NG]ns1 - alkali metals [NG]ns2 - alkaline earths [NG]ns2np1 [NG]ns2np2 [NG]ns2np3 [NG]ns2np4 - chalcogens [NG]ns2np5 - halogens [NG]ns2np6 - noble gases Malone and Dolter - Basic Concepts of Chemistry 9e 53 Transition Elements [NG]ns2(n-1)dy or [NG] (n-1)dyns2 - Transition elements NG is Ar, Kr, Xe or Rn [NG]ns2(n-1)dy(n-2)fz or [NG] (n-2)fz(n-1)dy ns2 - Inner transition elements NG is Xe or Rn Malone and Dolter - Basic Concepts of Chemistry 9e 54 Example 1 Consider the atom of sulfur (Z = 16) Sulfur has 16 electrons Electronic configuration is therefore 1s22s22p63s23p4 = [Ne] 3s23p4 Malone and Dolter - Basic Concepts of Chemistry 9e 55 Example 2 d and f subshells are used for heavier elements • Consider the atom of vanadium (Z = 23) Vanadium has 23 electrons Electronic configuration is therefore 1s22s22p63s23p63d34s2 = [Ar]3d34s2 Malone and Dolter - Basic Concepts of Chemistry 9e 56 Objective for Section 8-4 Using orbital diagrams, determine the distribution of electrons in an atom. Malone and Dolter - Basic Concepts of Chemistry 9e 57 8-4 Orbital Diagrams of the Elements Electrons act as if they are little magnets due to a property called spin, and they can have a spin up () or spin down (). The Pauli Exclusion Principle - two electrons can occupy the same orbital only if they have different spins. Malone and Dolter - Basic Concepts of Chemistry 9e 58 Orbital Diagrams of the Elements, Cont’d Hund’s Rule - when filling a subshell, electrons will avoid entering an orbital that already has an electron in it until there is no other alternative. Malone and Dolter - Basic Concepts of Chemistry 9e 59 Orbital Diagrams Represent the orbitals of the subshells as boxes and electrons as arrows. For second row representative elements Malone and Dolter - Basic Concepts of Chemistry 9e 60 Objective for Section 8-5 Using the periodic table, predict trends in atomic and ionic radii, ionization energy, and electron affinity. Malone and Dolter - Basic Concepts of Chemistry 9e 61 8-5 Periodic Trends Atomic radius is the distance from the nucleus to the outermost electrons. Atomic radii decrease across a period Atomic radii increase down a group The decrease from left to right in a period results from adding electrons to the same outer shell while protons are being added to the nucleus. All of the outer electrons are drawn closer to the nucleus. Malone and Dolter - Basic Concepts of Chemistry 9e 62 Atomic Radii (in pm) For metals, the numbers refer to single bond covalent radii Malone and Dolter - Basic Concepts of Chemistry 9e 63 Ionization Energy The energy required to remove an electron from a gaseous atom to form a gaseous ion is the 1st ionization energy (IE1) M(g) M+(g) + e- First ionization energies increase across a period. First ionization energies decrease down a group. Smaller atoms have higher first ionization energies (small atoms hold their electrons more tightly). Malone and Dolter - Basic Concepts of Chemistry 9e 64 Ionization Energies Metals are characterized by the relative ease that electrons are removed from them (low IE). Atoms can lose more than one electron: M+(g) M2+(g) + e- IE2 (2nd ionization energy). Successive ionization energies increase. Note that IE2 for Na, IE3 for Mg, and IE4 for Al are all very large compared to the preceding IE; see next slide and Table 8-2. Malone and Dolter - Basic Concepts of Chemistry 9e 65 Ionization Energies for the First Twenty Elements Malone and Dolter - Basic Concepts of Chemistry 9e 66 Ionization Energies The abnormally high ionization energies correspond to removing an electron from a completely filled shell E.g. from ns2np6 or ns2 These shells, corresponding to electron configurations of noble gases, can be considered to be especially stable. Malone and Dolter - Basic Concepts of Chemistry 9e 67 Electron Affinity (EA) Electron attachment energy (EAE) is that associated with the reaction X(g) + e- → X-(g); EAE It is negative if the anion is stable. Electron affinity is the energy needed to remove an electron from an anion to produce a neutral atom (all in the gas phase): the reverse of above X-(g) → X(g) + e-; EA While some electron affinities are zero or negative (for unstable anions), many are positive - in contrast to ionization energies. Malone and Dolter - Basic Concepts of Chemistry 9e 68 Ion Sizes When atoms lose electrons, the remaining electrons are more strongly attracted to the nucleus, hence cations are smaller than the atom. Anions hold the electrons less tightly, so they are larger. Malone and Dolter - Basic Concepts of Chemistry 9e 69 Core vs. Valence Electrons Removing an electron from an inner shell is energetically very costly. Removing electrons from the valence shell requires quite a bit less energy. This will have consequences for the formation of compounds. Malone and Dolter - Basic Concepts of Chemistry 9e 70