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Quantum Mechanical Model. Quantum Numbers, Periodic Trends

Quantum Mechanical Model. Quantum Numbers, Periodic Trends. H Chemistry I Unit 3. Objectives #1-7 The Development of a New Atomic Model. I. Electromagnetic Radiation

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Quantum Mechanical Model. Quantum Numbers, Periodic Trends

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  1. Quantum Mechanical Model. Quantum Numbers, Periodic Trends H Chemistry I Unit 3

  2. Objectives #1-7 The Development of a New Atomic Model I. Electromagnetic Radiation *scientists in the late 1800’s and early 1900’s discovered that passing an electric current through gases of various elements caused electromagnetic radiation to be emitted from the gas; some examples include

  3. Objectives #1-7 The Development of a New Atomic Model

  4. Objectives #1-7 The Development of a New Atomic Model *additional testing showed that EMR of energies too low or too high to see with the eye were also produced *electromagnetic radiation is energy that travels in the form of a wave *example diagram: (see lecture guide)

  5. Examples of Electromagnetic Waves

  6. Objectives #1-7 The Development of a New Atomic Model *characteristics of EMR: *the wavelength of a wave is the distance between the peaks of the wave *the frequency of a wave is the number of peaks that pass by a point is space in one second (the rate of reproducibility) *the speed of all EMR is the speed of light (3.00 X 108 m/s)

  7. Objectives #1-7 The Development of a New Atomic Model *wavelength and frequency are inversely related to each other c=f *frequency and energy are directly related to each other E=h *wavelength and energy are inversely related to each other E=hc/

  8. Objectives #1-7 The Development of a New Atomic Model Low Energy High Energy Radio Radar Micro IR Visible* UV X-rays Gamma *red, orange, yellow, green, blue, indigo, violet II. The Origins of Wave Mechanics *EMR has dual qualities: (Louis DeBroglie, 1892-1987), French

  9. Louis DeBroglie, 1892-1987), French

  10. Albert Einstein, 1905, German-American)

  11. Objectives #1-7 The Development of a New Atomic Model *it acts as a particle when it interacts with matter; this is illustrated by the photoelectric effect which involves the emission of electrons when radiation of a specific frequency strikes the surface of a metal (Albert Einstein, 1905, German-American) =hv0 *it acts as a wave when it travels through space =h/mv *matter also has particle and wave characteristics *Atomic Emission Spectrum (an explanation of the colors produced by exciting atoms) (Niels Bohr, 1885-1962, Danish)

  12. Photoelectric Effect

  13. Wave Particle Duality

  14. Objectives #1-7 The Development of a New Atomic Model =h/mv *matter also has particle and wave characteristics *Atomic Emission Spectrum (an explanation of the colors produced by exciting atoms) (Niels Bohr, 1885-1962, Danish)

  15. Niels Bohr, 1885-1962, Danish)

  16. Examples of Atomic Emission Spectrums

  17. Objectives #1-7 The Development of a New Atomic Model *Diagram: *an electron is normally in its low energy state or ground state *when the electron becomes excited with a certain amount of energy or quantum, it will “jump” to a higher level of energy or its excited state *this new state is unstable for the electron and so this excess energy is emitted as a photon of EMR and the electron returns to the ground state

  18. The Bohr Model and Electron Transitions Illustrated

  19. Objectives #1-7 The Development of a New Atomic Model • The Bohr Model of the Atom *proposed that electrons revolve around the nucleus in definite paths or orbits *each electron has a certain amount of energy associated with it *electrons are confined to specific energy levels *in order to move from one level to the next, an electron must absorb or release a certain quantum of energy

  20. The Bohr Model

  21. Erwin Schrodinger, 1887-1961, Austrian

  22. Objectives #1-7 The Development of a New Atomic Model *Bohr Diagrams: (examples) • The Quantum Mechanical Model of the Atom *Erwin Schrodinger, 1887-1961, Austrian *also proposed that electrons traveled in energy levels *proposed the quantum mechanical model for electrons

  23. Evolution of the Bohr Model into the Quantum Mechanical Model

  24. Werner Heisenberg, 1901-1976, German

  25. Objectives #1-7 The Development of a New Atomic Model *the exact path of the electron can not be determined because it is traveling near the speed of light and is too small in size *this idea was based on the work of Werner Heisenberg, 1901-1976, German *in the Heisenberg Uncertainty Principle there is a limit to how certain we can be about the position and speed of very tiny particles such as electrons

  26. Heisenberg Uncertainty Principle

  27. Objectives #1-7 The Development of a New Atomic Model *in the quantum model only the probability of finding the electron in a certain area can be determined *the most highly probable location for an electron about the nucleus is the orbital *the combination of these areas about the nucleus is called the electron cloud

  28. Orbital Shapes

  29. Objectives #8-10 Quantum Numbers • Schrodinger’s Equation: -h2/2m(ð2Ψ/ðx2 + ðΨ/ðy2 + ð2Ψ/ðz2) + V(x, y, z)Ψ = EΨ (neat huh?) *solving the previous equation produces various orbital shapes similar to: Y=1/2x + 2

  30. Objectives #8-10 Quantum Numbers • Quantum Numbers *describe energy and location of electrons *every electron in an atom is unique; each electron has a different energy and therefore will have a different set of quantum numbers

  31. Objectives #8-10 Quantum Numbers • Principle Quantum Number (n) *indicates energy and distance from nucleus *indicates energy level number *can take on values of: 1 → infinity • Orbital (Angular Momentum) Quantum Number (l) *indicates shape of orbital *can take on values of: 0, 1, 2, 3, n-1 *possible orbital shapes:

  32. Objectives #8-10 Quantum Numbers

  33. Objectives #8-10 Quantum Numbers *the number of orbital shapes in a level is equal to the level number:

  34. Objectives #8-10 Quantum Numbers and so on… • Magnetic Quantum Number (ml) *indicates the orientation of the orbital in space *indicates the number of orbitals in a sublevel *can take on values of: 0, +/- ℓ

  35. Objectives #8-10 Quantum Numbers

  36. Objectives #8-10 Quantum Numbers • Spin Quantum Number (ms) *indicates the direction of electron spin *can take on values of: +1/2, -1/2 *no more than 2 electrons can occupy a single orbital III. Problems Involving Quantum Numbers

  37. Objectives #8-10 Quantum Numbers IV. Summary of Electron Energy Level Capacities (examples) *some relationships to notice: if “n” is the number of levels, then the number of sublevels is equal to “n” if “n” is the number of levels, then the total number of orbitals in a level is equal to n2 if “n” is the number of levels (and every orbital can hold up to 2 electrons), then the total number of electrons in a level is equal to 2n2

  38. Objectives #11-12 Electron Configurations *electron configurations show electron arrangement • Rules Governing Electron Configurations • The Aufbau Principle *electrons enter orbitals of lowest energy first • The Pauli Exclusionary Principle *an atomic orbital may describe at most 2 electrons

  39. Aufbau Principle

  40. Pauli Exclusionary Principle and Hund’s Rule

  41. Objectives #11-12 Electron Configurations • Hund’s Rule *electrons enter orbitals of the same energy with the same spin until each orbital contains one electron before pairing begins • Examples of Electron Configurations / Orbital Notations / Noble-gas Configurations *Diagonal Rule: *More Examples: *Noble-gas configurations: *Exceptions to the Aufbau Principal (Diagonal Rule)

  42. The Diagonal Rule (an application of the Aufbau Principle)

  43. Objectives #13-19 The Periodic Table / Periodicity of Properties • Development of the Periodic Table *the work of Mendeleev (1871, Russian) elements were grouped by their properties; allowed for prediction of new elements; elements arranged by increasing atomic mass *the work of Moseley (1911, English): used X-ray studies to determine atomic numbers of elements and arranged in order of increasing atomic number

  44. Dimitri Mendeleev (1871, Russian)

  45. Henry Moseley (1911, English)

  46. Objectives #13-19 The Periodic Table / Periodicity of Properties Evolution of the Periodic Table

  47. Dimitri Mendeleev’s Periodic Table - 1871

  48. Periodic Table of 1930 Based on Henry Moseley’s Work

  49. Modern Periodic Table Based on the Work of Glenn Seaborg, 1951

  50. Organization of Modern Periodic Table *metals *nonmetals *metalloids *Main-group (representative elements) *Alkali Metals *Alkali Earth Metals *Halogens *Noble Gases *Transition Metals *Rare Earth Metals *Lanthanides *Actinides

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