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Modern Theory of the Atom: Quantum Mechanical Model

Modern Theory of the Atom: Quantum Mechanical Model. Recap of Bohr Model. electrons: particles moving in circular orbits with specific speed, position, & energy. energy levels possess specific quantum of energy. electrons can move between energy levels

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Modern Theory of the Atom: Quantum Mechanical Model

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  1. Modern Theory of the Atom:Quantum Mechanical Model

  2. Recap of Bohr Model • electrons: • particles moving in circular orbits with specific speed, position, & energy energy levels possess specific quantum of energy • electrons can move between energy levels • higher energy levels farther from nucleus • e- moving up to higher E level: electron absorbs energy • e- moving down to lower E level: electron emits light energy • ground state: • electrons located in lowest possible energy levels, closest can be to nucleus

  3. DeBroglie Electron-Wave Proposed this Idea: if light can show both particle and wave behavior, maybe matter can too wavelength describing electron depends on energy of electron at certain energies, electron waves make standing waves in atom wave does not represent path of electron

  4. Standing Wave confined to given space (ends are pinned) interference between incident & reflected waves at certain frequencies: certain points seem to be standing still other points - displacement changes in regular way 2 kinds of waves Traveling Wave • wave not confined to given space • travels from one location to another • interrupted by hitting boundary or another wave

  5. Transverse (ocean) Longitudinal (compressed/sound)

  6. electron = wave e– path is orbital holds 2 electrons not necessarily circular each orbit has specific energy probable location Bohr Model vs. Modern Theory • electron = particle • e- path is orbit • holds 2n2 electrons • circular path • each orbit has specific energy • can find exact position/ speed

  7. Heisenberg uncertainty principle • fundamentally impossible to know velocity & position of particle at same time • impossible to make observation without influencing system • cannot specify both position & speed of electron • can only determine probability of electron’s location in given region of space

  8. Orbital – Modern Theory • orbital: term describes region where e- might be found • each orbital: • specific energy & specific shape • described by 4 parameters of wave function (like an address) • quantum numbers = n, l, m, s • structure of orbitals explain: • bonding, magnetism, atom size, crystal structure

  9. n: principal quantum number • specifies atom’s principalenergy levels • whole number values: 1, 2, 3, 4, … • 2n2 = maximum # electrons in any principal energy level

  10. l = describes sublevels • sublevels are labelled by shape: • s, p, d, f

  11. s orbitals: spherical

  12. p orbitals: dumbbell shaped

  13. d orbitals: complex shapes

  14. f orbitals: complex shapes too

  15. Sublevels 1st principal energy level: s (1 sublevel) 2nd level: s,p (2 sublevels) 3rd level: s,p,d (3 sublevels) 4th level: s,p,d,f (4 sublevels)

  16. m = 3rd quantum number(orbitals) • each sublevel contains 1 or more orbitals • each orbital holds a max of 2 electrons • s has 1 orbital • p has 3 orbitals • d has 5 orbitals • f has 7 orbitals 1st PEL =s (1 sublevel) = 1 orbital (__ electrons) 2nd PEL =s,p (2 sublevels) = 4 orbitals (__ e-) 3rd PEL = s,p,d (3 sublevels) = 9 orbitals (___ e-) 4th PEL s,p,d,f (4 sublevels) = 16 orbitals (___ e-) 2 8 18 32

  17. 4th quantum number = s • e- spin: 2 possible values • clockwise and counter clockwise • Illustrated by arrows with opposite directions • 

  18. address for each electron • 4 quantum numbers • no 2 e- can • occupy the same space in atom • canhave same 4 quantum numbers therefore only 2 electrons per orbital (Pauli exclusion principle)

  19. Memorize sublevels # of orbitals sp d f 13 57 2e- 6e-10e- 14e- max # of electrons *each orbital holds 2 e- s p d f

  20. electron configurations • add e- to atoms so that e- are in lowest energy levels – most stable or ground state configuration • start with 1s, then work upward in order of increasing energy • use Aufbau rule.

  21. 3rd principal energy level, 3 sublevels 2nd principal energy level, 2 sublevels – s & p  1st principal energy level, 1 sublevel – s Each box represents an orbital and holds 2 electrons

  22. Aufbau Principle follow arrows sequence of orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, … exceptions do occur: - half-filled orbitals have extra stability - magic # is 8 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f

  23. He C Mg Zn • 1s2 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d10 5f14 6s2 6p6 6d10 7s2 7p6 7d10 1s22s22p2 • 1s22s22p63s2 1s22s22p63s23p6 4s23d10

  24. from these modern configurations, we can figure out Bohr Configurations All you have to do is add up the electrons in each shell (energy level) He C Mg Zn • 1s2 1= 2 2 1s22s22p2 1= 22= 2+2 2 – 4 • 1s22s22p63s2 1= 2 2= 2+6 3= 2 2 – 8 –2 1s22s22p63s23p64s23d10 1= 2 2= 2+6 3= 2+6+10 4=2 2 – 8 –18 –2

  25. Hund’s Rule • most e- with same spin, soif more than one same orbital: e- fill orbitals one at time before pairing up • 1s2 2s2 2p4

  26. Which element? How many unpaired e-? How many principal energy level’s occupied? How many principal energy level’s are fully occupied? How many sublevels contain e-? How many sublevels full? How many orbitals contain e-? Boron 1 2 1 3 2 3

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