(L3) electronic structure of atom

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(L3) electronic structure of atom

  1. 1. Electronic Structure of Atom Mr. Rumwald Leo G. Lecaros School of Chemical Engineering and Chemistry Mapua Institute of Technology 1
  2. 2. Outline  Quantum Theory  Photoelectric effect  Bohr’s Theory  Dual Nature of the Electrons  Quantum Mechanics  Quantum Numbers  Electronic Configuration (Part 2) 2
  3. 3. The Electromagnetic Spectrum  Visible light is a small portion of the electromagnetic radiation spectrum detected by our eyes.  Electromagnetic radiation includes radio waves, microwaves and X-rays.  Described as a wave traveling through space.  There are two components to electromagnetic radiation, an electric field and magnetic field. 3
  4. 4. The Wave Nature of Light  Wavelength, , is the distance between two corresponding points on a wave.  Amplitude is the size or “height” of a wave.  Frequency, , is the number of cycles of the wave passing a given point per second, usually expressed in Hz.
  5. 5. Planck’s Quantum Theory  Higher T = shorter λ (higher E) maximum.  Couldn’t explain with classical physics 5
  6. 6. Electromagnetic Radiation  In 1900 Max Planck studied black body radiation and realized that to explain the energy spectrum he had to assume that: 1. energy is quantized 2. light has particle character  Planck’s equation is 6 sJ10x6.626constantsPlanck’h hc or EhE 34-
  7. 7. The Wave Nature of Light  The fourth variable of light is velocity.  All light has the same speed in a vacuum.  c = 2.99792458 x 108 m/s  The product of the frequency and wavelength is the speed of light.  Frequency is inversely proportional to wavelength. 7 c
  8. 8. The Wave Nature of Light  Refraction is the bending of light when it passes from one medium to another of different density.  Speed of light changes.  Light bends at an angle depending on its wavelength.  Light separates into its component colors. 8
  9. 9. The Wave Nature of Light  Electromagnetic radiation can be categorized in terms of wavelength or frequency.  Visible light is a small portion of the entire electromagnetic spectrum. 9
  10. 10. Example Problem 6.1  Neon lights emit an orange-red colored glow. This light has a wavelength of 670 nm. What is the frequency of this light? 10
  11. 11. The Particulate Nature of Light  Photoelectric effect: light striking a metal surface generates photoelectrons.  The light’s energy is transferred to electrons in metal.  With sufficient energy, electrons “break free” of the metal.  Electrons given more energy move faster (have higher kinetic energy) when they leave the metal. 11
  12. 12. The Particulate Nature of Light  Photoelectric effect is used in photocathodes.  Light strikes the cathode at frequency . Electrons are ejected if exceeds the threshold value 0.  Electrons are collected at the anode.  Current flow is used to monitor light intensity.
  13. 13. Photoelectric Experiments a) For > 0, the number of electrons emitted is independent of frequency. Value of 0 depends on metal used. b) As light intensity increases, the number of photoelectrons increases. c) As frequency increases, kinetic energy of emitted electrons increases linearly. d) The kinetic energy of emitted electrons is independent of light intensity.
  14. 14. The Particulate Nature of Light  The photoelectric effect is not explained using a wave description but is explained by modeling light as a particle.  Wave-particle duality - depending on the situation, light is best described as a wave or a particle.  Light is best described as a particle when light is imparting energy to another object.  Particles of light are called photons.  Neither waves nor particles provide an accurate description of all the properties of light. Use the model that best describes the properties being examined. 14
  15. 15. The Particulate Nature of Light  The energy of a photon (E) is proportional to the frequency ( ).  and is inversely proportional to the wavelength ( ).  h = Planck’s constant = 6.626 x 10-34 J s 15 E h hc
  16. 16. Example Problem 6.2  The laser in a standard laser printer emits light with a wavelength of 780.0 nm. What is the energy of a photon of this light? 16
  17. 17. The Particulate Nature of Light  Binding Energy - energy holding an electron to a metal.  Threshold frequency, o - minimum frequency of light needed to emit an electron.  For frequencies below the threshold frequency, no electrons are emitted.  For frequencies above the threshold frequency, extra energy is imparted to the electrons as kinetic energy.  Ephoton = Binding E + Kinetic E  This explains the photoelectric effect. 17
  18. 18. Example Problem 6.3  In a photoelectric experiment, ultraviolet light with a wavelength of 337 nm was directed at the surface of a piece of potassium metal. The kinetic energy of the ejected electrons was measured as 2.30 x 10-19 J. What is the electron binding energy for potassium? 18
  19. 19. Atomic Spectra  Atomic Spectra: the particular pattern of wavelengths absorbed and emitted by an element.  Wavelengths are well separated or discrete.  Wavelengths vary from one element to the next.  Atoms can only exist in a few states with very specific energies.  When light is emitted, the atom goes from a higher energy state to a lower energy state. 19
  20. 20. Atomic Spectra  Electrical current dissociates molecular H2 into excited atoms which emit light with 4 wavelengths.
  21. 21. Atomic Spectra and the Bohr Atom  Every element has a unique spectrum.  Thus we can use spectra to identify elements.  This can be done in the lab, stars, fireworks, etc. 21
  22. 22. Example Problem 6.4  When a hydrogen atom undergoes a transition from E3 to E1, it emits a photon with = 102.6 nm. Similarly, if the atom undergoes a transition from E3 to E2, it emits a photon with = 656.3 nm. Find the wavelength of light emitted by an atom making a transition from E2 to E1. 22
  23. 23. The Bohr Atom  Bohr model - electrons orbit the nucleus in stable orbits. Although not a completely accurate model, it can be used to explain absorption and emission.  Electrons move from low energy to higher energy orbits by absorbing energy.  Electrons move from high energy to lower energy orbits by emitting energy.  Lower energy orbits are closer to the nucleus due to electrostatics. 23
  24. 24. The Bohr Atom  Excited state: grouping of electrons that is not at the lowest possible energy state.  Ground state: grouping of electrons that is at the lowest possible energy state.  Atoms return to the ground state by emitting energy as light. 24
  25. 25. Atomic Spectra and the Bohr Atom  The Rydberg equation is an empirical equation that relates the wavelengths of the lines in the hydrogen spectrum. 25 hydrogenofspectrumemission in thelevelsenergytheof numberstherefer tosn’ nn m101.097R constantRydbergtheisR n 1 n 1 R 1 21 1-7 2 2 2 1
  26. 26. Atomic Spectra and the Bohr Atom Example 4-8. What is the wavelength of light emitted when the hydrogen atom’s energy changes from n = 4 to n = 2? 26 2 1 2 2 1 2 7 -1 2 2 7 -1 7 -1 7 -1 6 -1 n 4 and n 2 1 1 1 R n n 1 1 1 1.097 10 m 2 4 1 1 1 1.097 10 m 4 16 1 1.097 10 m 0.250 0.0625 1 1.097 10 m 0.1875 1 2.057 10 m
  27. 27. Atomic Spectra and the Bohr Atom  In 1913 Neils Bohr incorporated Planck’s quantum theory into the hydrogen spectrum explanation.  Here are the postulates of Bohr’s theory. 27 1. Atom has a number of definite and discrete energy levels (orbits) in which an electron may exist without emitting or absorbing electromagnetic radiation. As the orbital radius increases so does the energy 1<2<3<4<5......
  28. 28. Atomic Spectra and the Bohr Atom 2. An electron may move from one discrete energy level (orbit) to another, but, in so doing, monochromatic radiation is emitted or absorbed in accordance with the following equation. 28 EE hc hEE-E 12 12 Energy is absorbed when electrons jump to higher orbits. n = 2 to n = 4 for example Energy is emitted when electrons fall to lower orbits. n = 4 to n = 1 for example
  29. 29. Atomic Spectra and the Bohr Atom 3. An electron moves in a circular orbit about the nucleus and it motion is governed by the ordinary laws of mechanics and electrostatics, with the restriction that the angular momentum of the electron is quantized (can only have certain discrete values). angular momentum = mvr = nh/2 h = Planck’s constant n = 1,2,3,4,...(energy levels) v = velocity of electron m = mass of electron r = radius of orbit 29
  30. 30. Atomic Spectra and the Bohr Atom  Light of a characteristic wavelength (and frequency) is emitted when electrons move from higher E (orbit, n = 4) to lower E (orbit, n = 1).  This is the origin of emission spectra.  Light of a characteristic wavelength (and frequency) is absorbed when electrons jump from lower E (orbit, n = 2) to higher E (orbit, n= 4)  This is the origin of absorption spectra. 30
  31. 31. Atomic Spectra and the Bohr Atom  Bohr’s theory correctly explains the H emission spectrum.  The theory fails for all other elements because it is not an adequate theory. 31
  32. 32. The Wave Nature of the Electron In 1925 Louis de Broglie published his Ph.D. dissertation.  A crucial element of his dissertation is that electrons have wave-like properties.  The electron wavelengths are described by the de Broglie relationship. 32 particleofvelocityv particleofmassm constantsPlanck’h mv h
  33. 33. The Wave Nature of the Electron Example 4-9. Determine the wavelength, in m, of an electron, with mass 9.11 x 10-31 kg, having a velocity of 5.65 x 107 m/s.  Remember Planck’s constant is 6.626 x 10-34 Js which is also equal to 6.626 x 10-34 kg m2/s. 33m1029.1 m/s1065.5kg109.11 ss/mkg10626.6 mv h 11 731- 2234
  34. 34. The Quantum Mechanical Picture of the Atom  Werner Heisenberg in 1927 developed the concept of the Uncertainty Principle.  It is impossible to determine simultaneously both the position and momentum of an electron (or any other small particle).  Detecting an electron requires the use of electromagnetic radiation which displaces the electron!  Electron microscopes use this phenomenon 34
  35. 35. The Quantum Mechanical Model of the Atom  Quantum mechanical model replaced the Bohr model of the atom.  Bohr model depicted electrons as particles in circular orbits of fixed radius.  Quantum mechanical model depicts electrons as waves spread through a region of space (delocalized) called an orbital.  The energy of the orbitals is quantized like the Bohr model. 35
  36. 36. The Quantum Mechanical Model of the Atom  Diffraction of electrons shown in 1927.  Electrons exhibit wave-like behavior.  Wave behavior described using a wave function, the Schrödinger equation.  H is an operator, E is energy and is the wave function. 36 H E
  37. 37. Potential Energy and Orbitals  Total energy for electrons includes potential and kinetic energies.  Potential energy more important in describing atomic structure; associated with coulombic attraction between positive nucleus and negative electrons.  Multiple solutions exist for the wave function for any given potential interaction.  n is the index that labels the different solutions. 37 H n E n
  38. 38. Potential Energy and Orbitals  n can be written in terms of two components.  Radial component, depends on the distance from the nucleus.  Angular component, depends on the direction or orientation of electron with respect to the nucleus. 38
  39. 39. Potential Energy and Orbitals  The wave function may have positive and negative signs in different regions.  Square of the wave function, 2, is always positive and gives probability of finding an electron at any particular point.  Each solution of the wave function defines an orbital.  Each solution labeled by a letter and number combination: 1s, 2s, 2p, 3s, 3p, 3d, etc.  An orbital in quantum mechanical terms is actually a region of space rather than a particular point. 39
  40. 40. Quantum Numbers  Quantum numbers - solutions to the functions used to solve the wave equation.  Quantum numbers used to name atomic orbitals.  Vibrating string fixed at both ends can be used to illustrate a function of the wave equation. 40
  41. 41. Quantum Numbers  When solving the Schrödinger equation, three quantum numbers are used.  Principal quantum number, n (n = 1, 2, 3, 4, 5, …)  Secondary quantum number, l  Magnetic quantum number, ml 41
  42. 42. Quantum Numbers  The principal quantum number, n, defines the shell in which a particular orbital is found.  n must be a positive integer  n = 1 is the first shell, n = 2 is the second shell, etc.  Each shell has different energies. 42
  43. 43. Quantum Numbers  The secondary quantum number, l, indexes energy differences between orbitals in the same shell in an atom.  l has integral values from 0 to n-1.  l specifies subshell  Each shell contains as many l values as its value of n. 43
  44. 44. Quantum Numbers  The energies of orbitals are specified completely using only the n and l quantum numbers.  In magnetic fields, some emission lines split into three, five, or seven components.  A third quantum number describes splitting. 44
  45. 45. Quantum Numbers  The third quantum number is the magnetic quantum number, ml.  ml has integer values.  ml may be either positive or negative.  ml’s absolute value must be less than or equal to l.  For l = 1, ml = -1, 0, +1 45
  46. 46. Quantum Numbers  Note the relationship between number of orbitals within s, p, d, and f and ml.
  47. 47. Example Problem 6.5  Write all of the allowed sets of quantum numbers (n, l, and ml) for a 3p orbital. 47
  48. 48. Visualizing Orbitals  s orbitals are spherical  p orbitals have two lobes separated by a nodal plane.  A nodal plane is a plane where the probability of finding an electron is zero (here the yz plane).  d orbitals have more complicated shapes due to the presence of two nodal planes.
  49. 49. Visualizing Orbitals  Nodes are explained using the Uncertainty Principle.  It is impossible to determine both the position and momentum of an electron simultaneously and with complete accuracy.  An orbital depicts the probability of finding an electron.  The radial part of the wave function describes how the probability of finding an electron varies with distance from the nucleus.  Spherical nodes are generated by the radial portion of the wave function. 49
  50. 50. Visualizing Orbitals  Cross sectional views of the 1s, 2s, and 3s orbitals.
  51. 51. Visualizing Orbitals  Electron density plots for 3s, 3p, and 3d orbitals showing the nodes for each orbital.
  52. 52. End of Part 1 52
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