Quantum Mechanics - Chapter 7 The Quantum-Mechanical The...

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Unformatted text preview: Chapter 7 The Quantum-Mechanical The Model of the Atom Model Read/Study: Chapter 7 in your textbook! Chapter Study/Master: Class Lecture Notes Class 1 Massive Brain Power – Solvay Conference 1927 Solvay 40 48 43 69 60 74 27 25 35 48 42 2 ATOMIC STRUCTURE Definition of Chemistry: The study of the properties, composition, and STRUCTURE of matter, the physical and chemical changes it undergoes, and the energy liberated or absorbed during those changes. The foundation for the STRUCTURE of inorganic STRUCTURE materials is found in the STRUCTURE of the atom. STRUCTURE Material Properties Bulk Structure Molecular Structure Atomic Structure 3 ATOMIC STRUCTURE Historical Development: Greek Concepts of Matter Aristotle - Matter is continuous, infinitely divisible, and is composed of only 4 elements: Earth, Air, Fire, and Water u Won the philosophical/political battle. u Dominated Western Thought for Centuries. u Seemed very “logical”. u Was totally WRONG!! WRONG!! Review Chapter 2 Discussions! 4 ATOMIC STRUCTURE The “Atomists” (Democritus, Lucippus, Epicurus, et. al.) - Matter consists ultimately of “indivisible” particles called “atomos” that canNOT be further subdivided or simplified. If these “atoms” had space between them, nothing was in that space - the “void”. u Lost the philosophical/political battle. u Lost to Western Thought until 1417. u Incapable of being tested or verified. u Believed the “four elements” consisted of “transmutable” atoms. u Was a far more accurate, though quite imperfect “picture” of reality. 5 ATOMIC STRUCTURE Modern Concepts of Matter John Dalton (1803) - An atomist who formalized the idea of the atom into a viable scientific theory in order to explain a large amount of empirical data that could not be explained otherwise. u Matter is composed of small “indivisible” particles called “atoms”. u The atoms of each element are identical to each other in mass but different from the atoms of other u elements. A compound contains atoms of two or more elements bound together in fixed proportions by mass. 6 ATOMIC STRUCTURE u A chemical reaction involves a rearrangement of of atoms but atoms are not created nor destroyed during such reactions. Present Concepts - An atom is an electrically neutral entity consisting of negatively charged electrons (e-) situated outside of a dense, positively charged nucleus consisting of positively charged protons (p+) and neutral neutrons (n0). Particle Particle Electron Proton Neutron Charge -1 +1 0 Mass Mass 9.109 x 10 -28 g 1.673 x 10 -24 g 1.675 x 10 -24 g 7 ATOMIC STRUCTURE Nucleus Model of a Helium-4 (4He) atom e- p+no no p+ eElectron Cloud How did we get this concept? - This portion of our program is brought to you by: Democritus, Dalton, Thompson, Planck, Einstein, Millikan, Democritus, Rutherford, Bohr, de Broglie, Heisenberg, Schrödinger, Chadwick, and many others. CHRISTMAS CHRISTMAS 8 Democritus Review Chapter 2 Discussions! 9 John Dalton 10 J. J. Thompson 11 J. J. Thompson’s Cathode Ray Experiments 12 ATOMIC STRUCTURE Democritus - First atomic ideas Dalton - 1803 - First Atomic Theory J. J. Thompson - 1890s - Measured the charge/mass ratio of the electron (Cathode Rays) Fluorescent Material _ Cathode + Anode Electric Field Source (Off) With the electric field off, the cathode ray is not deflected. 13 ATOMIC STRUCTURE - Cathode + Anode Fluorescent Material + Electric Field Source (On) With the electric field on, the cathode ray is deflected away from the negative plate. The stronger the electric field, the greater the amount of deflection. Cathode + Anode Magnet 14 ATOMIC STRUCTURE With the magnetic field present, the cathode ray is deflected out of the magnetic field. The stronger the magnetic field, the greater the amount of deflection. e/m = E/H2r e = the charge on the electron m = the mass of the electron E = the electric field strength H = the magnetic field strength r = the radius of curvature of the electron beam Thompson, thus, measured the charge/mass ratio Thompson, of the electron - 1.759 x 108 C/g of 1.759 15 ATOMIC STRUCTURE Summary of Thompson’s Findings: u Cathode rays had the same properties no matter Cathode what metal was being used. what u Cathode rays appeared to be a constituent of all Cathode matter and, thus, appeared to be a “sub-atomic” matter particle. particle. u Cathode rays had a negative charge. Cathode u Cathode rays have a charge-to-mass ratio Cathode of 1.7588 x 108 C/g. of 16 ATOMIC STRUCTURE R. A. Millikan - Measured the charge of the electron. In his famous “oil-drop” experiment, Millikan was able to determine the charge on the electron independently of its mass. Then using Thompson’s charge-to-mass ratio, he was able to calculate the mass of the electron. e = 1.602 10 x 10-19 coulomb e/m = 1.7588 x 108 coulomb/gram 28 m = 9.1091 x 10--28 gram gram Goldstein - Conducted “positive” ray experiments that lead to the identification of the proton. The charge was found to be identical to that of the electron and the mass was found to be 1.6726 x 10-24 g. 1.6726 17 ATOMIC STRUCTURE Ernest Rutherford - Developed the “nuclear” model of the atom. The Plum Pudding Model of the atom: A smeared out “pudding” of positive charge with negative electron “plums” imbedded in it. The Metal Foil Experiments: Radioactive Material in Pb box. α -particles Fluorescent Screen Metal Foil 18 19 ATOMIC STRUCTURE If the plum pudding model is correct, then all of the massive α -particles should pass right through without being deflected. In fact, most of the α - particles DID pass right In through. However, a few of them were deflected at high angles, disproving the “plum pudding” model. Rutherford concluded from this that the atom consisted of a very dense nucleus containing all of the sisted positive charge and most of the mass surrounded positive electrons that orbited around the nucleus much as the planets orbit around the sun. 20 ATOMIC STRUCTURE Problems with the Rutherford Model: It was known from experiment and electromagnetic theory that when charges are accelerated, they continuously emit radiation, i.e., they loose energy continuously. The “orbiting” electrons in the atom were, obviously, not doing this. u Atomic spectra and blackbody radiation were known to be DIScontinuous. DIS u The atoms were NOT collapsing. 21 ATOMIC STRUCTURE Atomic Spectra - Since the 19th century, it had Atomic Since been known that when elements are heated until they emit light (glow) they emit that light only at discrete frequencies, giving a line spectrum. discrete line - + Hydrogen Gas Line Spectrum 22 Spectroscopy 23 Spectroscopy Emission Spectra Absorption Spectra 24 ATOMIC STRUCTURE When white light is passed through a sample of the vapor of an element, only discrete frequencies are absorbed, giving a absorption ban spectrum. are absorption These frequencies are identical to those of the These line spectrum of the same element. line For hydrogen, the spectroscopists of the 19th Century found that the lines were related by the Rydberg equation: ν/ c = R[(1/m2) - (1/n2)] )] ν = frequency c = speed of light R = Rydberg Constant m = 1, 2, 3, …. n = (m+1), (m+2), (m+3), …. 25 Overview Color and Spectroscopy 26 ATOMIC STRUCTURE Max Planck - In 1900 he was investigating the nature of black body radiation and tried to interpret his findings using accepted theories of electromagnetic radiation (light). He was NOT successful since these theories were based on the assumption that light had WAVE characteristics. WAVE To solve the problem he postulated that light was emitted from black bodies in discrete packets he called “quanta”. Einstein later called them “photons”. By assuming that the atoms of the black body emitted energy only at discrete frequencies, he was able to explain black body radiation. E= 27 ATOMIC STRUCTURE Both spectroscopy and black body radiation indicated that atoms emitted energy only at indicated discrete frequencies or energies rather than discrete continuously. Is light a particle or a wave?? Why do atoms emit only discrete energies? What actually happens when light interacts with matter? What was wrong with Rutherford’s Model? 28 ATOMIC STRUCTURE Niels Bohr - Bohr corrected Rutherford’s model of the atom by formulating the following postulates: u Electrons in atoms move only in discrete orbits around the nucleus. u When in an orbit, the electron does NOT emit energy. u They may move from one orbit to another but are NEVER residing in between orbits. u When an electron moves from one orbit to another, it absorbs or emits a photon of light with a specific energy that depends on the distance between the two orbits. 29 ATOMIC STRUCTURE Balmer Series (Visible) Paschen Series + Lyman Series (UV) (IR) The Bohr Model of the Atom 30 Bohr Atom 31 ATOMIC STRUCTURE u The lowest possible energy state for an electron is called the GROUND STATE. All other states GROUND are called EXCITED STATES. EXCITED En = (- 2.179 x 10-18 J)/n2 Ephoton = Efinal - Einitial Ephoton = [(- 2.179 x 10-18 J)/n2final] -[(- 2.179 x 10-18 J)/n2initial] -[(= - 2.179 x 10-18 J[(1/n2final) - (1/n2initial)] 2.179 Does this equation look familiar? ν/ c = R[(1/m2) - (1/n2)] 32 Bohr Atom 33 ATOMIC STRUCTURE Niels Bohr won the Nobel Prize for his work. However, the model only worked perfectly for hydrogen. What about all of those other elements?? What Louis de Broglie - Thought that if light, which was thought to have wave characteristics, could also have particle characteristics, then perhaps electrons, which were thought to be particles, could have characteristics of waves. λ = h/mv where “mv” is momentum where An electron in an atom was a “standing wave”! 34 ATOMIC STRUCTURE Werner Heisenberg - Developed the “uncertainty” principle: It is impossible to make simultaneous and It exact measurements of both the position (location) and the momentum of a sub-atomic particle such as an electron. (∆ x)(∆ p) > h/2π Our knowledge of the inner workings of atoms and molecules must be based on probabilities rather than on absolute certainties. Erwin Schödinger - Developed a form of quantum mechanics known as “Wave Mechanics”. 35 ATOMIC STRUCTURE Wave Function - A mathematical function associated with each possible state of an electron in an atom or molecule. u It can be used to calculate the energy of an electron in the state u the average and most probable distance from the nucleus u the probability of finding the electron in any specified region of space. 36 ATOMIC STRUCTURE Quantum Numbers: Principle Quantum Number, n - An integer Principle greater than zero that represents the principle energy level or “shell” that an electron occupies. n 1 2 3 4 etc. Energy Level 1st 2nd 3rd 4th etc. Shell K L M N etc. # of orbitals n2 1 4 9 16 etc. 37 ATOMIC STRUCTURE Azimuthal Quantum Number, l - The quantum Azimuthal number that designates the “subshell” an electron occupies. It is an indicator of the shape of an orbital in the subshell. It has integer values from 0 to n-1. to l = 0, 1, 2, 3, 4, …, n - 1 s p d f g…. Magnetic Quantum Number, ml - The quantum number that determines the behavior of an electron in a magnetic field. It has integer values from -l to -l +l including 0. ml = -l, …, -3, -2, -1, 0, +1, +2, +3, …, +l 38 ATOMIC STRUCTURE n 1 2 l 0 0 1 3 0 1 2 etc. etc. Orbital Name 1s 2s 2p 2p 3s 3p 3p 3d etc. ml 0 0 -1, 0, +1 0 -1, 0, +1 -2, -1, 0, +1, -2, etc. etc. # of Orbitals 1 1 3 1 3 +2 5 etc. Spin Quantum Number, ms - The quantum number that designates the orientation of an electron in a magnetic field. It has half-integer values, +½ or -½. +½ 39 ATOMIC STRUCTURE So what do atoms look like? A. Interpretation of Ψ : The probability of finding probability an electron in a small volume of space centered around some point is proportional to the value of Ψ 2 at that point. B. Electron Probability Density vs. r C. Dot Density Representation: Imagine superimposing millions of photographs taken of an electron in rapid succession. D. Radial Densities 40 So what do atoms look like? 41 ATOMIC STRUCTURE 42 43 ATOMIC STRUCTURE 44 ATOMIC STRUCTURE 45 46 47 48 Chapter 8 Periodic Properties of the Elements Read/Study: Chapter 8 in e-Textbook! Chapter Study/Master: Class Lecture Notes Class 49 ATOMIC STRUCTURE ATOMIC Electron Configuration A. Many-electron atom: An atom that contains two or more electrons. B. Problems with the Bohr model: 1. It “assumed” quantization of the energy levels in hydrogen. 2. It failed to describe or predict the spectra of more complicated atoms. 50 C. What are the differences in electron energy levels in hydrogen vs. more complicated atoms? 3s 3p 2s 3d 2p Ground State Hydrogen Atom 1s 51 Splitting of the Degeneracy 2s 2p 2s 2p 1s 1s H Li 52 Splitting of the Degeneracy 1. In hydrogen, all subshells and orbitals in a given principal energy level have the same energy. They are said to be Degenerate. Degenerate 2. In many-electron atoms, s-orbitals have lower energy than p-orbitals which have lower energy than d-orbitals which have lower energy than f-orbitals, etc., etc. 3. Reason: Complex electrostatic interactions. 53 + - - - - - Hydrogen ++ Helium +++ Lithium A. Shielding Effect - A decrease in the nuclear force of attraction for an electron caused by the presence of other electrons in underlying orbitals. B. Effective Nuclear Charge - A positive charge that may be less than the atomic number. It is the charge “felt” by outer electrons due to shielding by electrons in underlying orbitals. 54 The Pauli Exclusion Principle - No two electron in No the same atom can have the same four quantum numbers. H + e- → H Quantum Number n l ml Electron 1 Electron 2 1 0 0 1 0 0 ms +1/2 -1/2 55 The Aufbau Principle - A procedure for “building up” the electronic configuration of many-electron atoms wherein each electron is added consecutively to the lowest energy orbital available, taking into account the Pauli exclusion principle. Order of Filling 1s 2s 2p 3s 1s 1s 2s 3s 4s 5s 3p 4s 3d 4p 5s Increasing Energy 2p 3p 3d 4p 4d 4f 5p 5d 5f 5g 56 Designating Electron Configurations u Standard Designation Standard H 1s1 Li 1s2 2s1 B 1s2 2s2 2p1 1s 2p He 1s2 Be 1s2 2s2 C 1s2 2s2 2p2 1s 2p u Orbital Diagram Designation Orbital H Li 1s He 1s 2s Be 1s B 1s 2s 2p 1s 2s 2p C 1s 2s 57 u Core Designation - A designation of electronic configuration wherein the outer shell electrons are shown along with the “core” configuration of the closest previous noble gas. Li [He] 2s1 Be [He] 2s2 Na [Ne] 3s1 Mg [Ne] 3s2 K Ca [Ar] 4s2 Rb [Ar] 4s1 [Kr] 5s 1 Sr [Kr] 5s2 58 59 60 What Element is Represented Below? 61 62 CORE 63 CORE 64 First Two Transition Metal Rows 65 Hund’s Rule of Maximum Multiplicity - Electrons occupy a given subshell singly and with parallel spins until each orbital in the subshell has one electron. “Electrons try to stay as far apart as possible” u Elevator Analogy B [He] 2s2 2p1 [He] C [He] 2s2 2p2 [He] N [He] 2s2 2p3 u Bus Seat Analogy [He] 2s 2p 66 The Structure of the Periodic Table u Historical Development - Dimitri Mendeleev and Lothar Meyer independently found that when the elements are ordered according to their atomic masses, similar properties recur periodically. Were they right? periodically Were u The Periodic Law - The properties of the elements are periodic functions of their atomic number. number u Physical Structure of the Table 67 Electronic Configuration and the Periodic Table u s-Block Elements s-Block u p-Block Elements p-Block u d-Block Elements d-Block u f-Block Elements f-Block Assignment: Write the electron configuration using Assignment: Write all three types of designation for lead (Pb). Electronic Configuration for positive ions (cations) Cations are formed by removing electrons in order of decreasing n value. Electrons with the same n value are removed in order of decreasing l value. 68 Electronic Configuration and the Periodic Table u s-Block Elements s-Block u p-Block Elements p-Block u d-Block Elements d-Block u f-Block Elements f-Block Assignment: Write the electron configuration using Assignment: Write all three types of designation for lead (Pb). 10 Pb 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 4p 6s 5d10 6p2 Pb [Xe] 6s2 4f14 5d10 6p2 (You do the orbital diagram Pb 6s designation!) 69 70 The properties of the elements are determined in large measure by their Atomic Number and their large Atomic Electron Configuration. u Paramagnetism - A property that arises from unpaired electrons in an atom or molecule. It is identified by the fact that when the element is placed in a magnetic field in a magnetic susceptibility experiment, the atom or molecule is drawn into the field. Assignment: Name the elements of the first 40 Assignment: elements in the Periodic Table that are diamagnetic. 71 u Atomic Size Atomic Atomic radii are considered to be 1/2 of the average distance between centers of identical atoms that are touching each other. This will vary with the chemical environment the atom is in. 142 pm 154 pm Fluorine Diamond C - 77 pm F - 71 pm 72 73 Trends in Atomic Radii: 1. Atomic radii increase from top to bottom in a increase family or group. The number of electrons and the nuclear charge are increasing! - Tends to shrink atom. But extra electron are added to new shells that are further from the nucleus and more effectively shielded from the nucleus - Tends to make the atom larger. 74 75 2. Atomic radii decrease from left to right decrease across a row or period. The number of electrons and the nuclear charge are increasing! - Tends to shrink atom. The electrons are being added to the same same shell and are not well shielded and thus, the atoms get smaller. 3. Summary of trends Down a Group - Larger Down Larger Across a Period - Smaller Across Smaller 76 What Affects Atomic/Ionic Sizes? ¡ The Charge on the Nucleus The ¡ Shielding - This reduces the actual nuclear This charge resulting in an “effective” nuclear charge. 77 4. Some Exceptions Al - Ga The Lanthanide Contraction u Ionic Size Ionic Based on the internuclear distance of cations and anions in ionic crystals. Not easy to determine how to apportion this distance between the cation and the anion. 78 Cations - Monatomic cations are smaller than smaller their parent atoms. q The whole outer shell is typically removed. q The effective nuclear charge is increased. Na atom 186 pm Na+ ion 102 pm 79 Ionic Sizes 80 Anions - Monatomic anions are larger than larger their parent atoms. q The extra electrons are typically added to the same shell where they are repelled by the other electrons already present, making the ion bigger than its parent atom. F Atom 71 pm Fluoride Ion 136 pm 81 Ionic Sizes 82 u Ionization Energy - The energy required to The remove an electron from a gaseous groundstate atom or ion. A. First Ionization Energy - The energy required to remove the most loosely bound electron from the valence shell. B. Second Ionization Energy - The energy required to remove the second electron after the first one is gone. C. Third Ionization Energy - Etc., Etc., Etc. 83 Li (g) (g) Li+ + e- IE1 = +520 kJ/mol Li+ Li2+ + e- IE2 = +7298 kJ/mol Na (g)Na+ (g) + e- IE1 = +496 kJ/mol Na+ Na2+ + e- Na2+ Na3+ + e- Mg (g) (g) Mg+ + e- Mg+ Mg2+ + e- Mg2+ Mg3+ + e- IE2 = +4564 kJ/mol IE3 = +6918 kJ/mol IE1 = +737 kJ/mol IE2 = +1447 kJ/mol IE3 = +7738 kJ/mol84 Trends in First Ionization Energies 85 Trends in Ionization Energies 86 u Electron Affinity - The energy absorbed when absorbed an electron is added to a gaseous ground-state atom or ion. It has the same sign as the ∆ H of atom the process. Cl (g) + e - Cl - ∆ H = - 349 kJ/mol E.A. = - 349 kJ/mol Some other textbooks use a different sign convention for the E.A. You need to be aware of that when you are reading about this topic. In those texts, the electron affinity for a chlorine atom would be + 349 kJ/mol! 87 F (g) + e - F- E.A. = - 328 kJ/mol O (g) + e - O- E.A. = - 141 kJ/mol O- + O 2- E.A. = + 880 kJ/mol e- O (g) + 2 e (g) 2 O 2-- E.A. = + 739 kJ/mol ∆ H = + 739 kJ/mol So then why does oxygen usually have a -2 oxidation state instead of a -1 oxidation state (Oxides are more common than peroxides)??? Na (g) + e - Na - E.A. = - 53 kJ/mol ∆ H = - 53 kJ/mol 88 Trends in Electron Affinities Increases up a group. Increases up Increases from left to right in a period. Increases from 89 ...
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This note was uploaded on 10/23/2010 for the course BIOL 2308 taught by Professor Boxer during the Spring '10 term at University of Houston - Downtown.

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