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Chapter 6 Electronic Structure of Atoms

CHEMISTRY The Central Science 9th Edition. Chapter 6 Electronic Structure of Atoms. 6.1: The Wave Nature of Light. Electromagnetic Radiation carries energy through space Speed of EMR through a vacuum: 3.00x10 8 m/s wavelike characteristics:

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Chapter 6 Electronic Structure of Atoms

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  1. CHEMISTRYThe Central Science 9th Edition Chapter 6Electronic Structure of Atoms Chapter 6

  2. 6.1: The Wave Nature of Light • Electromagnetic Radiation carries energy through space • Speed of EMR through a vacuum: 3.00x108 m/s • wavelike characteristics: • wavelength, l (distance from crest to crest) • amplitude, A (height) • frequency, n(# of cycles which pass a point in 1 second) Chapter 6

  3. The # of times the cork bobs up and down is the frequency The wave nature is due to periodic oscillations of the intensities of electronic and magnetic forces associated with the radiation Chapter 6

  4. Text, P. 200 Frequency and wavelength are inversely related

  5. The speed of a wave, c, is given by its frequency multiplied by its wavelength: • For light, speed = c (that is 3.00 x 108m/s) Chapter 6

  6. Modern atomic theory arose out of studies of the interaction of radiation with matter • Example: the visible spectrum Chapter 6

  7. The Electromagnetic Spectrum, P. 201 (or Hz)

  8. Text, P. 201 Chapter 6

  9. Sample Problem #7 Chapter 6

  10. 6.2: Quantized Energy and Photons • Problems with wave theory: • Emission of light from hot objects • “black body radiation”: stove burner, light bulb filament • The photoelectric effect • Emission spectra Chapter 6

  11. Planck: energy can only be absorbed or released from atoms in certain amounts called quanta • The relationship between energy and frequency is • where h is Planck’s constant (6.626  10-34 J-s) Chapter 6

  12. Quantization Analogy: • Consider walking up a ramp versus walking up stairs: • For the ramp, there is a continuous change in height • Movement up stairs is a quantized change in height Chapter 6

  13. The Photoelectric Effect • Evidence for the particle nature of light -- “quantization” • Light shines on the surface of a metal: electrons are ejected from the metal • threshold frequency must be reached • Below this, no electrons are ejected • Above this, the # of electrons ejected depends on the intensity of the light Chapter 6

  14. Text, P. 204

  15. Einstein assumed that light traveled in energy packets called photons • The energy of one photon: • Energy and frequency are directly proportional • Therefore radiant • energy must be quantized! Chapter 6

  16. Sample Problems # 13, 17, 19 Chapter 6

  17. 6.3: Line Spectra and the Bohr Model • Line Spectra • Radiation that spans an array of different wavelengths: continuous • White light through a prism: continuous spectrum of colors • Spectra tube emits light unique to the element in it • Looking at it through a prism, only lines of a few wavelengths are seen • Black regions correspond to wavelengths that are absent Chapter 6

  18. Continuous Visible Spectrum, P. 206

  19. Chapter 6

  20. Bohr Model • Rutherford model of the atom: electrons orbited the nucleus like planets around the sun • Physics: a charged particle moving in a circular path should lose energy • Therefore the atom should be unstable Chapter 6

  21. 3 Postulates for Bohr’s theory: • Electrons move in orbits that have defined energies • An electron in an orbit has a specific energy • Energy is only emitted or absorbed by an electron as it changes from one allowed energy state to another (E=hν) Chapter 6

  22. Since the energy states are quantized, • the light emitted from excited atoms must be quantized and appear as line spectra • Bohr showed that • where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else) Chapter 6

  23. The first orbit in the Bohr model has n = 1, is closest to the nucleus, and has the lowest energy (ground state) • The furthest orbit in the Bohr model has n close to infinity Chapter 6

  24. Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (hν) • The amount of energy absorbed or emitted on movement between states is given by • Sample Problems # 21 and 27 Chapter 6

  25. Line Spectra, P. 207 Note the units The Balmer series for Hydrogen (nf = 2, which is in the visible region) nf values for other regions of the EMS: Lyman (UV): nf = 1 Paschen (IR): nf = 3 Brackett (IR): nf = 4 Pfund (IR): nf = 5 The Rydberg Equation (P. 206) allows for the calculation of wavelengths for all the spectral lines n = energy level Chapter 6

  26. Paschen Series Balmer Series Energy Level Diagram Lyman Series Figure 6.14, P. 208 Using the Rydberg Equation, the existence of spectral lines can be attributed to the quantized jumps of electrons between energy levels (therefore justifying Bohr’s model of the atom) Sample Problems # 29 and 31

  27. The Electromagnetic Spectrum, P. 201 (or Hz) Chapter 6

  28. Limitations of the Bohr Model • It can only explain the line spectrum of hydrogen adequately • Electrons are not completely described as small particles • It doesn’t account for the wave properties of electrons • DEMOS! Chapter 6

  29. 6.4:The Wave Behavior of Matter • Using Einstein’s and Planck’s equations, de Broglie showed: • The momentum, mv, is a particle property, but  is a wave property • Sample Exercise 6.5, P. 210 Chapter 6

  30. The Uncertainty Principle • Heisenberg’s Uncertainty Principle: we cannot determine exactly the position, direction of motion, and speed of an electron simultaneously Chapter 6

  31. 6.5: Quantum Mechanics and Atomic Orbitals • Erwin Schrödinger proposed an equation that contains both wave and particle terms • Solving the equation leads to wave functions (shape of the electronic orbital) Chapter 6

  32. Text, P. 213 The electron density distribution in the ground state of the hydrogen atom Chapter 6

  33. Orbitals and Quantum Numbers • If we solve the Schrödinger equation, we get wave functions and energies for the wave functions. • We call wave functions orbitals (regions of highly probable electron location). • Schrödinger’s equation requires 3 quantum numbers: • Principal Quantum Number, n • This is the same as Bohr’s n. • As n becomes larger, the atom becomes larger and the electron is further from the nucleus. • Orbitals and Quantum Numbers • If we solve the Schrödinger equation, we get wave functions and energies for the wave functions • We call wave functions orbitals (regions of highly probable electron location) • Schrödinger’s equation requires 3 quantum numbers: • Principal Quantum Number, n • This is the same as Bohr’s n • As n becomes larger, the atom becomes larger and the electron is further from the nucleus Chapter 6

  34. 2. Azimuthal Quantum Number, l • This quantum number depends on the value of n • The values of l begin at 0 and increase to (n - 1) • We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3) • Usually we refer to the s, p, d and f-orbitals (the shape of the orbital) (AKA “subsidiary quantum number”) • 3. Magnetic Quantum Number, ml • This quantum number depends on l • The magnetic quantum number has integral values between -l and +l • Magnetic quantum numbers give the 3D orientationof each orbital Chapter 6

  35. As n increases, note that the spacing between energy levels becomes smaller “Aufbau Diagram”: electrons fill low energy orbitals first Figure 6.17, P. 215 Chapter 6

  36. Sample Problems # 41, 43, & 45 Chapter 6

  37. 6.6: Representations of Orbitals • The s-Orbitals • All s-orbitals are spherical • As n increases, the s-orbitals get larger Chapter 6

  38. the s orbitals Text, P. 216 Chapter 6

  39. The p-Orbitals • There are three p-orbitalspx, py, and pz • The three p-orbitals lie along the x-, y- and z- axes of a Cartesian system • The letters correspond to allowed values of ml of -1, 0, and +1 • The orbitals are dumbbell shaped • As n increases, the p-orbitals get larger Chapter 6

  40. the p orbitals Text, P. 216 Chapter 6

  41. The d and f-Orbitals • There are five d and seven f-orbitals • FYI for the d-orbitals: • Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes • Two of the d-orbitals lie in a plane aligned along the x-, y- and z-axes • Four of the d-orbitals have four lobes each • One d-orbital has two lobes and a collar • Text, P. 217 Chapter 6

  42. the d orbitals Text, P. 217

  43. the f orbitals (not in text) Chapter 6

  44. http://www.uky.edu/~holler/html/orbitals_2.html Chapter 6

  45. Text, P. 214 (-l to +l) Max = (n-1) l  letter (n2) (# of orientations) Chapter 6

  46. 6.7: Many-Electron Atoms • Orbitals and Their Energies • Orbitals of the same energy are said to be degenerate • For n 2, the s- and p-orbitals are no longer degenerate because the electrons interact with each other • Therefore, the Aufbau diagram looks slightly different for many-electron systems Chapter 6

  47. BOHR Text, P. 215 MODERN Text, P. 218

  48. Electron Spin and the Pauli Exclusion Principle • Since electron spin is also quantized, we define • ms = spin quantum # =  ½ Text, P. 219

  49. Pauli’s Exclusion Principle: no two electrons can have the same set of 4 quantum numbers • Therefore, two electrons in the same orbital must have opposite spins • Electron capacity of sublevel = 4l + 2 • Electron capacity of energy level = 2n2 Chapter 6

  50. Sample Problems # 51 & 55 Chapter 6

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