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Chemistry 101 : Chap. 6

Chemistry 101 : Chap. 6. Electronic Structure of Atoms. The Wave Nature of Light Quantized Energy and Photon (3) Line Spectra and Bohr Models (4) The Wave Behavior of Matter (5) Quantum Mechanics and Atomic Orbitals (6) Representations of Orbitals (7) Many Electron Atoms

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Chemistry 101 : Chap. 6

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  1. Chemistry 101 : Chap. 6 Electronic Structure of Atoms • The Wave Nature of Light • Quantized Energy and Photon • (3) Line Spectra and Bohr Models • (4) The Wave Behavior of Matter • (5) Quantum Mechanics and Atomic Orbitals • (6) Representations of Orbitals • (7) Many Electron Atoms • (8) Electron Configurations • (9) Electron Configurations and Periodic Table

  2. Electronic Structure  What is the electronic structure? The way electrons are arranged in an atom  How can we find out the electronic structure experimentally ? Analyze the light absorbed and emitted by substances  Is there a theory that explains the electronic structure of atoms? Yes. We need “quantum mechanics” to explain the results from experiments

  3. Wave Nature of Light • Electromagnetic Radiation : Visible lightis an example of electromagnetic radiation (EMR) Electric Field Magnetic Field

  4. Wave Nature of Light  Properties of EMR  All EMR have wavelike characteristics  Wave is characterized by its wavelength, amplitude and frequency EMR propagates through vacuum at a speed of 3.00  108 m/s (= speed of light = c)

  5. Wave Nature of Light  Frequency () and wavelength () Frequency measures how many wavelengths pass through a point per second:  4 complete cycles pass through the origin  = 4 s-1 = 4 Hz Note that the unit of  is m  = c 1 s

  6. Wave Nature of Light Higher frequency Longer wavelength

  7. Wave Nature of Light  Example : What is the wavelength, in m, of radio wave transmitted by the local radio station WHQR 91.3 MHz?

  8. Wave Nature of Light  Example : Calculate the frequency of radio wave emitted by a cordless phone if the wavelength of EMR is 0.33m.

  9. Physics in the late 1800’s Universe Matter (particles) Wave (radiation) F = ma Newton’s equation Maxwell’s equation James C. Maxwell (1831-1879) Isaac Newton (1643-1727)

  10. The Failure of Classical Theories In the late 1800, there were three important phenomena that could not be explained by the classical theories Black body radiation Photoelectric effect Line Spectra of atoms

  11. Black Body Radiation Hot objects emit light. The higher the temperature, the higher the emitted frequency • Black body : An object that absorbs all electromagnetic radiations that falls onto it. No radiation passes through it and none is reflected. The amount and wavelength of electromagnetic radiation a black body emits is directly related to their temperature.

  12. Black Body Radiation “Ultraviolet catastrophe” classical theory predicts significantly higher intensity at shorter wavelengths than what is observed. intensity wavelength (nm) visible region

  13. Black Body Radiation • Classical Theory :  Electromagnetic radiation has only wavelike characters. • Energy (or EMR) can be absorbed and emitted in any amount.  Planck’s Solution : He found that if he assumed that energy could only be absorbed and emitted in discrete amounts then the theoretical and experimental results agree. Max Planck (1858 - 1947)

  14. Quantization of Energy  Energy Quanta : Planck gave the name ``quanta’’ to the smallest quantity of energy that can be absorbed or emitted as EMR. E = h Energy of a quantum of EMR with frequency  frequency of EMR h = Planck Constant = 6.626  10-34 Js NOTE : Energy of EMR is related to frequency, not intensity NOTE : When energy is absorbed or emitted as EMR with a frequency , the amount of energy should be a integer multiple of h

  15. Quantization of Energy  Example : Calculate the energy contained in a quantum of EMR with a frequency of 95.1 MHz.

  16. Photoelectric Effect  Photoelectric Effect : When light of certain frequency strikes a metal surface electrons are ejected. The velocity of ejected electrons depend on the frequency of light, not intensity. K.E.of ejected electron = Energy of EMR  Energy needed to release an e- e- Light of a certain minimum frequency is required to dislodge electrons from metals e- e- e-

  17. Photoelectric Effect • Einstein’s Solution: In 1905, Einstein explained photoelectric effect by assuming that EMR can behave as a stream of particles, which he called photon. The energy of each photon is given by Ephoton = h        K.E.e = h   incident photon energy binding energy Kinetic energy of ejected electrons e- e- e- Einstein’s discovery confirmed Planck’s notion that energy is quantized.

  18. Energy, Frequency and Wavelength • Example : Calculate the energy of a photon of EMR with a wavelength of 2.00 m.

  19. EMR: Is it wave or particle? Einstein’s theory of light poses a dilemma: Is light a wave or does it consist of particles?  When conducting experiments with EMR using wave measuring equipment (like diffraction), EMR appear to be wave  When conducting experiments with EMR using particle techniques (like photoelectric effect), EMR appear to be a stream of particles EMR actually has both wavelike and particle-like characteristics. It exhibits different properties depending on the methods used to measure it.

  20. Continuous Spectrum  Many light sources, including light bulb, produce light containing many different wavelengths continuous spectrum

  21. Line Spectrum  When gases are placed under low pressure and high voltage, they produces light containing a few wavelengths.

  22. Line Spectrum  Rydberg equation: The positions of all line spectrum () can be represented by a simple equation. RH (Rydberg Constant) = 1.096776  107 m-1 (for hydrogen) n1 and n2 are integer numbers (n1 < n2)

  23. Line Spectrum  Example : Identify the locations of first three lines of hydrogen line spectrum

  24. Bohr Model of Hydrogen Atom • The electron is permitted to be in orbits of certain radii, • corresponding to certain definite energies. (2) When the electron is in such permitted orbits, it does not radiate and therefore it will not spiral into the nucleus. (3) Energy is emitted or absorbed by the electron only as the electron changes from one allowed state (or orbit) to another. This energy is emitted or absorbed as a photon, E=h

  25. Bohr Model of Hydrogen Atom principal quantum number ground state n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 excited states nucleus Bohr model proposed in 1913 Niels Bohr (1885 – 1962)

  26. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Bohr Model of Hydrogen Atom Question #1 : What is the energy of electron associated with each orbit?

  27. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Bohr Model of Hydrogen Atom Question #2 : How much energy will be absorbed or emitted when the electron changes it orbit between n1 and n3? n1 n3 : Einit < Efinal absorption n3 n1 : Einit > Efinal emission Energy e e Ground State Ground State h = | Einit - Efinal |

  28. Bohr Model of Hydrogen Atom  Example : How much energy will be absorbed or emitted for an electron transition from n=1 to n=3 ? What is the frequency of light associated with such transition? Is this result consistent with the Rydberg equation?

  29. Bohr Model of Hydrogen Atom Energy gap decreases as n increases Balmer series Why the hydrogen line spectra (above) shows only Balmer series, involving n=2? What happens to the transitions involving n=1? What is the meaning of n =  and E = 0?

  30. Limitations of Bohr Model • Bohr model does not work for atoms with more than • one electron Check out http://jersey.uoregon.edu/vlab/elements/Elements.html for emission and absorption spectra all elements in periodic table (2) There are more lines buried under the line spectrum of hydrogen. Bohr model of hydrogen can not explain such fine structure of hydrogen atom, which was discovered later.

  31. The Wave Behavior of Matter Electrons in Bohr model are treated as particles. In order to explain the electronic structure of atom, we need to incorporate the wave-like nature of electron into the theory. For a particle of mass m, moving with a velocity v, De Broglie Wavelength Louis de Broglie (1892-1987)

  32. The Wave Behavior of Matter  Example : What is the wavelength of an electron traveling at 1% of the speed of light? Repeat the calculation for a baseball moving at 10 m/s. (mass of electron = 9.11  10-31 kg, mass of baseball = 145 g)

  33. Quantum Mechanics Schrodinger developed a theory incorporating wave-like nature of particles (1) The motions of particles can be described by wavefunction, (r). (2) Wavefunction, (r), can tell us only the probability to locate the particle at the position r Schrodinger equation Werner Heisenberg (1901-1976) Erwin Schrodinger (1887-1961)

  34. Hydrogen Atom in Quantum Mechanics Probability to find a electron • The denser the stippling, the • higher the probability of finding • the electron

  35. z y x Bohr model vs. Quantum Mechanics Bohr’s model: n = 1 orbit electron circles around nucleus Quantum Mechanics: orbital n = 1 or electron is somewhere within that spherical region

  36. Bohr model vs. Quantum Mechanics Probability to find the electron at a distance r from the nucleus (green = Bohr model, Red = Quantum Mechanics) n = 1 n = 2 distance from nucleus (10-10 m) distance from nucleus (10-10 m)

  37. Bohr model vs. Quantum Mechanics Bohr’s model: requires only the principal quantum number (n) to describe an orbit Quantum Mechanics: needs three different quantum numbers to describe an orbital n : principal quantum number l : azimuthal quantum number ml : magnetic quantum number

  38. Bohr model vs. Quantum Mechanics Energy level diagam Quantum Mechanics Bohr model n=3 l = 2 Energy n=2 l = 1 n=1 l = 0

  39. Energy of electron in a given orbital : Principal Quantum Number  Principal quantum number, n, in quantum mechanicsis analogous to the principal quantum number in Bohr model n describes the general size of orbital and energy  The higher n, the higher the energy of the electron  n is always a positive integer: 1, 2, 3, 4 ….

  40. l is normally listed as a letter: Value of l: 0 1 2 3 letter: spdf Azimuthal Quantum Number  l takes integer values from 0 to n-1 e.g. l= 0, 1, 2 for n = 3 l defines the shape of an electron orbital

  41. l =1 p-orbital (1 of 3) l= 2 d-orbital (1 of 5) l = 3 f-orbital (1 of 7) Azimuthal Quantum Number z y x l = 0 s-orbital

  42. Magnetic Quantum Number ml takes integral values from -l to +l, including 0 ml= -2, -1, 0, 1, 2 e.g. forl = 2 ml describes the orientation of an electron orbital in space 2Py 2Px 2Pz

  43. Quantum Numbers  Example : Which of the following combinations of quantum numbers is possible? n=1, l=1, ml= -1 n=3, l=0, ml= -1 n=3, l=2, ml= 1 n=2, l=1, ml= -2

  44. Atomic Orbitals  Shell:  A set of orbitalswith the same principal quantum number, n  Total number of orbitals in a shell is n2  Subshells: Orbitals of one type(same l)within the same shell  A shell of quantum number n has n subshells

  45. Atomic Orbitals in H Atom  n=3 shell : It has 3 subshells (3s,3p,3d)  n=2 shell : It has 2 subshells (2s, 2p) There are 5 orbitals in this subshell Each orbital in this subshell has the same n and l quantum number, but different ml quantum number  n=1 shell : It has 1 subshell (1s)

  46. Atomic Orbitals  Example: Fill in the blanks in the following table Principal quantum Type of orbitals Total Number Number (n) (subshell) of orbitals 1 2 3 4

  47. Atomic Orbitals 3 dimensional representation of 1s, 2s, 3s orbitals 1s 2s 3s

  48. Atomic Orbitals 3 dimensional representation of 2p orbitals

  49. Atomic Orbitals 3 dimensional representation of 3d orbitals

  50. Electron Spin Quantum Number  Spin magnetic quantum number (ms) : A fourth quantum number that characterizes electrons: ms can only take two values, +1/2 or -1/2

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