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Chapter 7 Quantum Theory and Atomic Structure

Chapter 7 Quantum Theory and Atomic Structure. Read/Study: Chapter 7 Suggested Problems: Sample Problems - 7.1 - 7.7 Follow-up Problems – 7.1 – 7.7 Work as many of the End-of- Chapter problems as you can. Watch the Videos about “The Atom”!. ATOMIC STRUCTURE. Definition of Chemistry:.

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Chapter 7 Quantum Theory and Atomic Structure

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  1. Chapter 7Quantum Theory andAtomic Structure Read/Study:Chapter 7 Suggested Problems: Sample Problems - 7.1 - 7.7 Follow-up Problems – 7.1 – 7.7 Work as many of the End-of- Chapter problems as you can. Watch the Videos about “The Atom”!

  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 theSTRUCTUREof inorganic materials is found in theSTRUCTUREof the atom. 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 • Won the philosophical/political battle. • Dominated Western Thought for Centuries. • Seemed very “logical”. • Was totally WRONG!!

  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”. • Lost the philosophical/political battle. • Lost to Western Thought until 1417. • Incapable of being tested or verified. • Believed the “four elements” consisted of “transmutable” atoms. • 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. • Matter is composed of small “indivisible”particles called “atoms”. • The atoms of each element are identical to each other in mass but different from the atoms of other elements. • A compound contains atoms of two or more elements bound together in fixed proportions by mass.

  6. ATOMIC STRUCTURE • 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, posi- tively charged nucleus consisting of positively charged protons (p+) and neutral neutrons (n0). ParticleChargeMass Electron - 1 9.109 x 10 -28 g Proton +1 1.673 x 10 -24 g Neutron 0 1.675 x 10 -24 g

  7. ATOMIC STRUCTURE Nucleus Model of a Helium-4 (4He) atom p+no e- e- no p+ Electron Cloud How did we get this concept? - This portion of our program is brought to you by: Democritus, Dalton, Thompson, Planck, Einstein, Millikan, Rutherford, Bohr, de Broglie, Heisenberg, Schrödinger, Chadwick, and many others. CHRISTMAS

  8. 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.

  9. ATOMIC STRUCTURE - Fluorescent Material - Cathode + + Anode 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

  10. 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 of the electron - 1.759 x 108 C/g

  11. ATOMIC STRUCTURE • Summary of Thompson’s Findings: • Cathode rays had the same properties no matter what metal was being used. • Cathode rays appeared to be a constituent of all matter and, thus, appeared to be a “sub-atomic” particle. • Cathode rays had a negative charge. • Cathode rays have a charge-to-mass ratio of 1.7588 x 108 C/g.

  12. 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 m = 9.1091 x 10-28 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.

  13. 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. + + + + + + Electrons The Metal Foil Experiments: Fluorescent Screen a-particles Radioactive Material in Pb box. Metal Foil

  14. ATOMIC STRUCTURE If the plum pudding model is correct, then all of the massive a-particles should pass right through without being deflected. In fact, most of the a - particles DID pass right through. However, a few of them were deflected at high angles, disproving the “plum pudding” model. Rutherford concluded from this that the atom con- sisted of a very dense nucleus containing all of the positive charge and most of the mass surrounded electrons that orbited around the nucleus much as the planets orbit around the sun.

  15. 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. ATOMIC STRUCTURE Planck • Atomic spectra and blackbody radiation were known to be DIScontinuous. Bohr • The atoms were NOT collapsing.

  16. ATOMIC STRUCTURE Atomic Spectra - Since the 19th century, it had been known that when elements are heated until they emit light (glow) they emit that light only at discrete frequencies, giving a line spectrum. - + Hydrogen Gas Line Spectrum

  17. 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. These frequencies are identical to those of the line spectrum of the same element. For hydrogen, the spectroscopists of the 19th Century found that the lines were related by the Rydberg equation: n/c = R[(1/m2) - (1/n2)] n = frequency R = Rydberg Constant c = speed of light m = 1, 2, 3, …. n = (m+1), (m+2), (m+3), ….

  18. 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. 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 = hn = hn/l

  19. Both spectroscopy and black body radiation indicated that atoms emitted energy only at discrete frequencies or energies rather than continuously. ATOMIC STRUCTURE 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?

  20. Niels Bohr - Bohr corrected Rutherford’s model • of the atom by formulating the following postulates: • Electrons in atoms move only in discrete orbits around the nucleus. • When in an orbit, the electron does NOT emit energy. • They may move from one orbit to another but are NEVER residing in between orbits. • 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. ATOMIC STRUCTURE

  21. ATOMIC STRUCTURE Balmer Series (Visible) Lyman Series + Paschen Series (UV) (IR) The Bohr Model of the Atom

  22. ATOMIC STRUCTURE • The lowest possible energy state for an electron is called the GROUND STATE. All other states are called EXCITED STATES. 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)] Does this equation look familiar? n/c = R[(1/m2) - (1/n2)]

  23. 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?? 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. l = h/mv where “mv” is momentum An electron in an atom was a “standing wave”!

  24. Werner Heisenberg - Developed the “uncertainty” principle: It is impossible to make simultaneous and exact measurements of both the position (location) and the momentum of a sub-atomic particle such as an electron. ATOMIC STRUCTURE (Dx)(Dp) > h/2p 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”.

  25. ATOMIC STRUCTURE • Wave Function - A mathematical function associated • with each possible state of an electron in an atom or • molecule. • It can be used to calculate the energy of an • electron in the state • the average and most probable distance from the nucleus • the probability of finding the electron in any specified region of space. Y Y Y Y Y

  26. ATOMIC STRUCTURE Quantum Numbers: Principle Quantum Number, n - An integer greater than zero that represents the principle energy level or “shell” that an electron occupies. Energy # of orbitals n Level Shell n2 1 1st K 1 2 2nd L 4 3 3rd M 9 4 4th N 16 etc. etc. etc. etc.

  27. ATOMIC STRUCTURE Azimuthal Quantum Number, l - The quantum 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. 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 including 0. ml = -l, …, -3, -2, -1, 0, +1, +2, +3, …, +l

  28. Orbital # of n l Name ml Orbitals 1 0 1s 0 1 2 0 2s 0 1 1 2p -1, 0, +1 3 3 0 3s 0 1 1 3p -1, 0, +1 3 2 3d -2, -1, 0, +1, +2 5 etc. etc. etc. etc. etc. ATOMIC STRUCTURE 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.

  29. ATOMIC STRUCTURE So what do atoms look like? A. Interpretation of Y: Theprobability of finding an electron in a small volume of space centered around some point is proportional to the value of Y2at that point. B. Electron Probability Density vs. r C. Dot Density Representation: Imagine super- imposing millions of photographs taken of an electron in rapid succession. D. Radial Densities

  30. Chapter 8Electron Configuration andChemical Periodicity Read/Study:Chapter 8 Suggested Problems: Sample Problems 8.1 - 8.8 Follow-up Problems 8.1 - 8.8 End-of-Chapter Problems At least every 3rd problem. ChemSkill Builder Units 9 & 11

  31. ATOMIC STRUCTURE • 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.

  32. C. What are the differences in electron energy levels in hydrogen vs. more complicated atoms? 3s 3p3d Energy 2s 2p Ground State Hydrogen Atom 1s

  33. Splitting of the Degeneracy 2p 2s 2p 2s Energy 1s 1s Li H

  34. 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. 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.

  35. - - - - - + - ++ 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.

  36. The Pauli Exclusion Principle - No two electron in the same atom can have the same four quantum numbers. H + e- H - Quantum Electron 1 Electron 2 Number n 1 1 l 0 0 ml 0 0 ms +1/2 -1/2

  37. 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 3p 4s 3d 4p 5s Increasing Energy 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 5g mnemonic device

  38. Designating Electron Configurations - • Standard Designation H 1s1 He 1s2 Li 1s2 2s1 Be 1s2 2s2 B 1s2 2s2 2p1 C 1s2 2s2 2p2 • Orbital Diagram Designation H He Li Be B C 1s 2s 2s 2p 1s 1s 1s 2s 2p 1s 2s 1s

  39. 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 Na K Rb [He] 2s1 [He] 2s2 Be Mg Ca Sr [Ne] 3s1 [Ne] 3s2 [Ar] 4s1 [Ar] 4s2 [Kr] 5s1 [Kr] 5s2

  40. 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” • Elevator Analogy • Bus Seat Analogy [He] 2s2 2p1 [He] B C N [He] 2s2 2p2 [He] [He] 2s2 2p3 [He] 2s 2p

  41. The Structure of the Periodic Table • 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? • The Periodic Law - The properties of the elements are periodic functions of their atomic number. • Physical Structure of the Table

  42. Electronic Configuration and the Periodic Table • s-Block Elements • p-Block Elements • d-Block Elements • f-Block Elements Assignment: Write the electron configuration using 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.

  43. Electronic Configuration and the Periodic Table • s-Block Elements • p-Block Elements • d-Block Elements • f-Block Elements Assignment: Write the electron configuration using all three types of designation for lead (Pb). • Pb 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p66s2 4f14 • 5d10 6p2 • Pb [Xe] 6s2 4f14 5d10 6p2 (You do the orbital diagram designation!)

  44. The properties of the elements are determined in • large measure by their Atomic Number and their • Electron Configuration. • 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 elements in the Periodic Table that are diamagnetic.

  45. Atomic Size - 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

  46. Trends in Atomic Radii: • 1. Atomic radii increase from top to bottom in a • 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. The Winner!!

  47. 2. Atomic radii decrease from left to right • 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 shell and are not well shielded and thus, the atoms get smaller. • 3. Summary of trends • Down a Group - Larger • Across a Period - Smaller

  48. What Affects Atomic/Ionic Sizes? • The Charge on the Nucleus • Shielding - This reduces the actual nuclear charge resulting in an “effective” nuclear charge.

  49. 4. Some Exceptions • Al - Ga Eu & Yb • The Lanthanide Contraction • Ionic Size - • 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.

  50. Cations - Monatomic cations are smaller than • their parent atoms. • The whole outer shell is typically removed. • The effective nuclear charge is increased. Na atom 186 nm Na+ ion 102 nm

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