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Quantum Numbers

Quantum Numbers. Bohr model- required that electrons be confined to specific orbits which had specific corresponding energy. Bohr equation: n represents the number of each orbit, starting closest to the nucleus

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Quantum Numbers

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  1. Quantum Numbers

  2. Bohr model- required that electrons be confined to specific orbits which had specific corresponding energy

  3. Bohr equation: • nrepresents the number of each orbit, starting closest to the nucleus • His theory was widely accepted because the constants ended up to be equal to the Rydberg constant! And produced a model of the atom

  4. The energy difference between two given orbits is constant • The same amount of energy needed to promote an electron to a higher orbit, will be released when the electron drops back

  5. Wave mechanical model • Describing the motion of an electron- very complicated wave equations- Schroedinger Equation

  6. 6 new ideas…. • 1. The wave equations require 3 numbers-quantum numbers-in order to solve the equations

  7. Quantum numbers • n- principal quantum number • l- azimuthal quantum number • ml –magnetic quantum number • ms- spin quantum number

  8. 2. Changed the picture of the atom • Bohr’s fixed orbits replaced by a “cloud” • Modern orbit is a region of space in which the probability of finding the electron is the highest

  9. 3. Wave equations provide a shape for each of the clouds • 4. arrangements of electrons agrees with element arrangement of the periodic table • Deeper understanding of chemical properties based on shapes of clouds

  10. 5. Results of the wave equation agree completely with the Bohr model calculations • 6. Heisenberg Uncertainty Principal • Position and momentum of an electron cannot be exactly known at the same time

  11. Electron Configuration • Principal energy level – n (principal quantum number) • Energy level increases in size and energy the farther the electron is from the nucleus- can hold more electrons • Maximum number of electrons an energy level 2n2

  12. Sublevels - l- azimuthal quantum number (room type) • Each principal quantum energy level contains sublevels • # of sublevels = to the value of nfor that energy level • Ex: for the third principal energy level (n=3) contains a maximum of 3 sublevels • Sublevels 5, 6, and 7 are theoretically possible but not currently needed

  13. Sublevels are numbered with consecutive whole numbers starting with 0 • The value of l can never be greater than n-1 • Each number corresponds to a letter s,p,d, or f (room type s,p,d,f)

  14. Orbitals • Each sublevel can contain one or more electron orbitals • Orbital-region of space that has high electron density and each orbital may contain a MAXIMUM of 2 electrons

  15. Orbitals • To share an orbital the 2 electrons must have opposite spins (Pauli Exclusion Principle) • ms - values for spin can be +1/2 or -1/2 • When 2 electrons share an orbital they are “paired” • Orbitals have the same designation as the sublevel they are in (s,p,d,f)

  16. The number of orbitals that a sublevel can have depends on the azimuthal quantum number, l • Can have 2l + 1 orbitals

  17. ml magnetic quantum number (room number) • Each orbital is given a number that range from - l to +l including 0

  18. Electron Configurations A list of all the electrons in an atom (or ion) • Must go in order (Aufbau principle) • 2 electrons per orbital, maximum • We need electron configurations so that we can determine the number of electrons in the outermost energy level. These are called valence electrons. • The number of valence electrons determines how many and what this atom (or ion) can bond to in order to make a molecule 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14…etc.

  19. Electron Configuration Rules • The ways in which electrons are arranged in various orbitals around the nuclei of atoms are called electron configurations. • Three rules—the aufbau principle, the Pauli exclusion principle, and Hund’s rule—tell you how to find the electron configurations of atoms.

  20. Aufbau Principle • electrons occupy the orbitals of lowest energy first. In the aufbau diagram below, each box represents an atomic orbital.

  21. Pauli Exclusion Principle • an atomic orbital may describe at most two electrons. To occupy the same orbital, two electrons must have opposite spins; that is, the electron spins must be paired.

  22. Hund’s Rule • states that electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible.

  23. 8A 1A 1 2A 3A 4A 5A 6A 7A 2 3 3B 4B 5B 6B 7B 8B 8B 8B 1B 2B 4 s d p 5 6 7 f 6 7 group # = # valence (outside) e- Row = # shells

  24. Why are d and f orbitals always in lower energy levels? • d and f orbitals require LARGE amounts of energy • It’s better (lower in energy) to skip a sublevel that requires a large amount of energy (d and f orbtials) for one in a higher level but lower energy This is the reason for the diagonal rule! BE SURE TO FOLLOW THE ARROWS IN ORDER!

  25. 8A 1A 1 2A 3A 4A 5A 6A 7A 2 3 3B 4B 5B 6B 7B 8B 8B 8B 1B 2B 4 d 5 6 7 f 6 7 Subshells d and f are “special” group # = # valence e- 3d period # = # e- shells 4d 5d 6d 4f 5f

  26. Electron Configuration 1s1 # of electrons in that subshell row # (on periodic table) Also known as shell # (principal quantum # n) possibilities are 1-7 7 rows subshell possibilities are s, p, d, or f 4 subshells

  27. Diagonal Rule • Must be able to write it for the test! This will be question #1 ! Without it, you will not get correct answers ! • The diagonal rule is a memory device that helps you remember the order of the filling of the orbitals from lowest energy to highest energy • _____________________ states that electrons fill from the lowest possible energy to the highest energy

  28. Order of Electron Subshell Filling:It does not go “in order” 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d10 5f14 6s2 6p6 6d10 7s2 7p6 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6

  29. Shorthand Notation • A way of abbreviating long electron configurations • Since we are only concerned about the outermost electrons, we can skip to places we know are completely full (noble gases), and then finish the configuration

  30. Paramagnetic Atoms • Lone atoms with one or more unpaired electrons and are attracted by magnetic fields • _____ _____ ____ ____ ____ 1s 2s 2p

  31. Diamagnetic Atoms • Lone atoms with NO unpaired electrons are repelled by magnetic fields • _____ _____ ____ ____ ____ 1s 2s 2p • Ex: Neon

  32. Iron

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