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Quantum Numbers

Quantum Numbers. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137. Very general – includes many cities. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137.

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Quantum Numbers

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  1. Quantum Numbers

  2. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137

  3. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137 Very general – includes many cities

  4. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137 Very general – includes many cities Still general – includes a handful of cities

  5. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137 Very general – includes many cities Still general – includes a handful of cities Specific, but includes many places

  6. How does a letter get to you? 5501 Haltom Rd Haltom City, TX 76137 Very specific – specifies only 1 place Very general – includes many cities Still general – includes a handful of cities Specific, but includes many places

  7. Quantum numbers are mathematical “addresses” of electrons for an atom – no two electrons can have the same exact address

  8. Summary Notes

  9. Quantum numbers are mathematical “addresses” of electrons for an atom – no two electrons can have the same exact address (n, l, ml, ms) => title

  10. Notes Summary • n = principle quantum number • energy level • relates to size • possible values are all positive integers (1 to ∞) • n = 1, 2, 3, 4, 5, 6, 7 • (seven periods on the periodic table)

  11. Notes Summary • l = azimuthal quantum number • sublevel • relates to shape • possible values are 0 to n-1 (currently 0-3) • s = 0 • p = 1 • d = 2 • f = 3

  12. ml = magnetic quantum number • orbitals • possible values are integers from –l to l • if l = 0 , then s = 0 • if l = 1, then p = -1, 0, 1 • if l = 2, then d = -2, -1, 0, 1, 2 • if l = 3, then f = -3, -2, -1, 0, 1, 2, 3 Notes Summary

  13. Notes Summary • ms = spin quantum number • spin of the electron • possible values are ½ and -½ • = ½ • = -½

  14. example – Ti (22 electrons) orbital notation ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ 1s 2s 2p 3s 3p 4s 3d

  15. example – Ti (22 electrons) orbital notation ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ 1s 2s 2p 3s 3p 4s 3d 1st arrow (1, 0, 0, ½)

  16. example – Ti (22 electrons) orbital notation ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ 1s 2s 2p 3s 3p 4s 3d 1st arrow (1, 0, 0, ½) 2nd arrow (1, 0, 0, -½)

  17. example – Ti (22 electrons) orbital notation ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ 1s 2s 2p 3s 3p 4s 3d 1st arrow (1, 0, 0, ½) 2nd arrow (1, 0, 0, -½) Can be combined into (1, 0, 0, ±½)

  18. ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ 1s 2s 2p 3s 3p 4s 3d 3rd and 4th arrows = (2, 0, 0, ±½)

  19. ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ 1s 2s 2p 3s 3p 4s 3d 3rd and 4th arrows = (2, 0, 0, ±½) for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

  20. ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ 1s 2s 2p 3s 3p 4s 3d 3rd and 4th arrows = (2, 0, 0, ±½) for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½) for 3s: (3, 0, 0, ±½)

  21. ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ 1s 2s 2p 3s 3p 4s 3d 3rd and 4th arrows = (2, 0, 0, ±½) for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½) for 3s: (3, 0, 0, ±½) for 3p: (3, 1, -1, ±½) and (3, 1, 0, ±½) and (3, 1, 1, ±½)

  22. ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ 1s 2s 2p 3s 3p 4s 3d 3rd and 4th arrows = (2, 0, 0, ±½) for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½) for 3s: (3, 0, 0, ±½) for 3p: (3, 1, -1, ±½) and (3, 1, 0, ±½) and (3, 1, 1, ±½) for 4s: (4, 0, 0, ±½)

  23. ___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___ • 1s 2s 2p 3s 3p 4s 3d • 3rd and 4th arrows = (2, 0, 0, ±½) • for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½) • for 3s: (3, 0, 0, ±½) • for 3p: (3, 1, -1, ±½) and (3, 1, 0, ±½) and (3, 1, 1, ±½) • for 4s: (4, 0, 0, ±½) • for 3d: (3, 2, -2, ½) and (3, 2, -1, ½) • notice -- no more arrows

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