Quantum Mechanic Model


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Quantum Mechanic Model

  1. 1. <ul><li>Four Quantum Numbers: </li></ul><ul><ul><li>Specify the “address” (zip code) of each electron in an atom </li></ul></ul>
  2. 2. <ul><li>First number…Principal Quantum Number ( n) </li></ul><ul><li>Energy level (associated with the electron) </li></ul><ul><li>Size if orbital </li></ul><ul><ul><li>Lowest energy level is assigned principle quantum number of 1 (n=1) </li></ul></ul><ul><ul><ul><li>Ground state </li></ul></ul></ul><ul><ul><li>What do you think happens as we increase n? </li></ul></ul><ul><ul><ul><li>Orbital becomes larger </li></ul></ul></ul><ul><ul><ul><li>Electron spends more time farther away from the nucleus  atom’s energy increases </li></ul></ul></ul>
  3. 3. Principle energy levels contain… Energy Sublevels
  4. 4. <ul><li>Principle energy level 1  single sublevel </li></ul><ul><li>Principle energy level 2  two sublevels </li></ul><ul><li>Principle energy level 3  three sublevels </li></ul><ul><li>What pattern do you see in the number of sublevels as we move further away from the nucleus? </li></ul><ul><ul><li>They increase as n increases (the further we get from the nucleus) </li></ul></ul>UPPER LEVEL
  5. 5. <ul><li>Electron’s are labeled according to n value </li></ul><ul><li>In atom’s with more than one electron, two or more electron’s may have the same n value </li></ul><ul><ul><li>They are in the same “electron shell” </li></ul></ul>
  6. 6. Second quantum number Angular Momentum Quantum Number (l)
  7. 7. <ul><li>Each value of l corresponds to a different type of orbital with a different shape </li></ul><ul><li>Value of n controls l (subshells possible) </li></ul><ul><li>Angular momentum numbers can equal 0, 1, 2, 3… </li></ul><ul><li>l=n-1 </li></ul><ul><ul><li>When n=1, l=0  only one possible subshell </li></ul></ul><ul><ul><li>When n=2, l=0,1  two possible subshells </li></ul></ul>
  8. 8. What the number of l means… <ul><li>Corresponds to the name of the subshell </li></ul><ul><ul><li>L=0  subshell s </li></ul></ul><ul><ul><li>L=1  subshell p </li></ul></ul><ul><ul><li>L=2  subshell d </li></ul></ul><ul><ul><li>L=3  subshell f </li></ul></ul>
  9. 9. S P D F: THE SUBLEVELS <ul><li>Each of these 4 sublevels has a unique shape </li></ul><ul><li>Each orbital may contain at most, 2 electrons </li></ul><ul><li>LETTERS ORIGINATED FROM DESCRIPTIONS OF THEIR SPECTRAL LINES </li></ul><ul><ul><li>S  sharp…spherical </li></ul></ul><ul><ul><li>P  principal…dumbbell shaped </li></ul></ul><ul><ul><li>D  diffuse…not all the same shape </li></ul></ul><ul><ul><li>F  fundamental…not all the same shape </li></ul></ul>
  10. 12. <ul><li>When principle energy level n=1, then l=0, which means there is only a single sublevel (one orbital) which is the small, spherical 1s </li></ul><ul><li>When principle energy level n=2, then l can equal 0 or 1, which means that there are two sublevels (orbitals) 2s and 2p </li></ul><ul><ul><li>2s sublevel  bigger than 1s, still sphere </li></ul></ul><ul><ul><li>2p sublevel  three dumbbell shaped p orbitals of equal energy called 2px, 2py, and 2pz </li></ul></ul><ul><ul><ul><li>The letters are just there to tell you what axis the electrons go on: x,y, or z axis </li></ul></ul></ul><ul><li>When the principle energy level n=3, then l can equal 0,1, or 2, which means that there are 3 possible sublevels: </li></ul><ul><ul><li>3s, sphere, bigger than 1s and 2s </li></ul></ul><ul><ul><li>3p, dumbbells </li></ul></ul><ul><ul><li>3d </li></ul></ul><ul><ul><ul><li>Each d sublevel consists 5 orbitals of equal energy </li></ul></ul></ul><ul><ul><ul><li>Four d orbitals have same shape but different orientations </li></ul></ul></ul><ul><ul><ul><li>Fifth d orbital, 3d z2 is shaped and oriented different from the other four </li></ul></ul></ul><ul><li>When the principle energy level n=4, then 1 can equal 0,1,2, or 3 which means l=n-1=4 possible sublevels: </li></ul><ul><ul><li>Seven f orbitals of equal energy ( 2 electrons in each orbital) </li></ul></ul><ul><ul><li>4s, sphere </li></ul></ul><ul><ul><li>4p, dumbbells </li></ul></ul><ul><ul><li>4d, </li></ul></ul><ul><ul><li>4f </li></ul></ul>
  11. 13. n = # of sublevels per level n 2 = # of orbitals per level Sublevel sets: 1 s, 3 p, 5 d, 7 f
  12. 16. Orbitals combine to form a spherical shape. 2s 2p z 2p y 2p x
  13. 17. Remember… <ul><ul><li>1. Principal #  energy level </li></ul></ul><ul><ul><li>2. Ang. Mom. #  sublevel (s,p,d,f) </li></ul></ul>There are two more quantum numbers (3 and 4) we will discuss next class
  14. 18. Third Quantum Number <ul><li>M l  specifies the orientation of the orbital in space containing the electron </li></ul><ul><li>Tells us whether the orbital is on the x, y, or z axis </li></ul>
  15. 19. Fourth Quantum Number <ul><li>M s  related to the direction of the electron spin </li></ul><ul><li>Tells us if electron has a clockwise spin or counter clockwise spin </li></ul><ul><li>Specifies orientation of electrons spin axis </li></ul>
  16. 20. Recap… <ul><li>Bohr? </li></ul><ul><ul><li>Orbits explained hydrogen’s quantized energy states </li></ul></ul><ul><li>De Broglie? </li></ul><ul><ul><li>Dual particle and wave nature of electrons </li></ul></ul><ul><li>Schrodinger? </li></ul><ul><ul><li>Wave equation predicted existence of atomic orbitals containing electrons </li></ul></ul>
  17. 21. Electron Configuration <ul><li>Definition: arrangement of electrons in an atom </li></ul><ul><li>Basic rules for filling up orbital's with electrons </li></ul><ul><li>Which is more stable, low energy or high energy? </li></ul><ul><ul><li>So which orbitals are going to be filled up first? </li></ul></ul><ul><ul><li>We are going to want an arrangement that gives us the lowest possible energy </li></ul></ul>
  18. 22. Ground state electron configuration <ul><li>The most stable, lowest energy electron arrangement of an atom </li></ul><ul><li>Each element has a ground-state electron configuration </li></ul>
  19. 23. Three Rules for Electron Arrangement <ul><li>Aufbau Principle </li></ul><ul><li>Pauli Exclusion Principle </li></ul><ul><li>Hund’s Rule </li></ul>
  20. 24. Aufbau Principle <ul><li>Each electron occupies the lowest energy orbital available </li></ul><ul><li>In order to do this, you must learn the sequence of atomic orbitals from lowest to highest energy </li></ul><ul><li>Aufbau Diagram </li></ul><ul><ul><li>Each box represents an orbital </li></ul></ul><ul><ul><li>Each arrow represents an electron </li></ul></ul><ul><ul><li>Only two arrows per box… </li></ul></ul><ul><ul><ul><li>Only two electrons per orbital </li></ul></ul></ul>
  21. 27. Some important things to remember about Aufbau… <ul><li>All orbitals related to an energy sublevel are of equal energy </li></ul><ul><ul><li>All three 2p orbitals have the same energy </li></ul></ul><ul><li>In a multi-electron atom, the energy sublevels within a principle energy level have different energies </li></ul><ul><ul><li>All three 2p orbitals are of higher energy than the one 2s orbital </li></ul></ul>
  22. 29. <ul><li>In order of increasing energies, the sequence of energy sublevels within a principle energy level is s, p, d, f </li></ul><ul><li>Orbitals related to energy sublevels within one principle energy level can overlap orbitals related to energy sublevels within another principle level </li></ul><ul><ul><li>Ex. An orbital related to the atoms 4s sublevel has a lower energy than the five orbitals related to 3d sublevel. </li></ul></ul>
  23. 31. Pauli Exclusion Principle <ul><li>States that a maximum on 2 electrons can occupy a single atomic orbital but only if the electrons have opposite spins </li></ul><ul><li>Wolfgang Pauli </li></ul><ul><li>Austrian Physicist </li></ul><ul><li>Observed atoms in excited states </li></ul>
  24. 32. <ul><li>Each electron has a spin </li></ul><ul><li>Kinda like a spinning top </li></ul><ul><li>It can only spin in one of 2 directions </li></ul><ul><li>In order for electrons to be together in an orbital, they must have opposite spins </li></ul>
  25. 33. Hund’s Rule <ul><li>What kind of charge do electrons have? </li></ul><ul><li>Do they attract or repel each other? </li></ul><ul><li>So…….. </li></ul><ul><li>Hund’s Rule states that single electrons with the same spin must occupy all each energy equal orbital before additional electrons with opposite spins can occupy the same orbital </li></ul>
  26. 34. 2p orbitals
  27. 35. Read section 5-3!