Quantum Numbers, Orbitals and Electron Configuration Ch' 4

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Quantum Numbers, Orbitals and Electron
Configuration (Ch. 4)

• Electrons Determine Properties and Bonding!
• Please have handy your periodic table, colored
  pencils, and quantum numbers organizing chart.

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Quantum Numbers

• Describe location of electrons around the nucleus
• Each atom has its own unique set of quantum
  numbers
• Like an address for the electrons
• Relates to periodic table

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Quantum Numbers

• Principal quantum number n, gives energy level of
  electron (whole number, 1 to infinitybut we use
  only 1-7)
• n 1
• n 2
• Etc..
• The higher the number, the farther away from the
  nucleus and the higher the energy.

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The horizontal rows of the periodic table are
called PERIODS.
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The vertical columns of the periodic table are
called GROUPS, or FAMILIES.
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Energy Levels Correspond with Period Numbers

• Energy levels closest to the nucleus (1) are
  smaller than those further out.
• Periods 1-7 are numbered for you on your periodic
  table down left margin. There is some overlap in
  other areas of the table. We will label the rest
  later.

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Sublevels

• Within each energy level there are sublevels.
• The energy level number (n) corresponds to the
  number of sublevels.

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• Energy level 1 has 1 sublevel
• Energy level 2 has 2 sublevels
• Energy level 3 has 3 sublevels
• Etc

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Quantum Numbers

• Secondary quantum number, l, describes the
  sublevel
• whole numbers from 0 to max. of n-1
• If n 1, l 0
• If n 2, l 0 or 1
• If n 3, l 0, 1, or 2
• If n 4, l 0, 1, 2, or 3, etc
• usually denoted by a letter, s, p, d, or f

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• Energy level 1 has 1 sublevel (s)
• Energy level 2 has 2 sublevels (s,p)
• Energy level 3 has 3 sublevels (s,p,d)
• Within each sublevel there are orbitals.
• The letter gives the shape of orbitals.

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• Sublevel s has 1 orbital that is spherical in
  shape.

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• Sublevel p has 3 orbitals that are dumb-bell
  shaped.

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• Sublevel d has 5 orbitals.

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• Sublevel f has 7 orbitals.

Click to view the Orbitron
http//www.shef.ac.uk/chemistry/orbitron/
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Quantum Numbers

• Angular momentum quantum number, ml , describes
  the orbital numbered l through 0 to l.
• If l 0 ml 0 (Energy level 3 has a single s
  orbital.)
• If l 1 then ml -1, 0, 1. This means energy
  level 3 also has 3 p orbitals.
• If l 2 then ml -2, -1, 0, 1, or 2. This
  means energy level 3 also has 5 d orbitals.

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Quantum Numbers

• If n 4, l 0, 1, 2 or 3.
• If l 0 ml 0 (Energy level 4 has a single s
  orbital.)
• If l 1 then ml -1, 0, 1. This means energy
  level 4 also has 3 p orbitals.
• If l 2 then ml -2, -1, 0, 1, or 2. This
  means energy level 4 also has 5 d orbitals.
• If l 3 then ml -3, -2, -1, 0, 1, 2, or 3.
  This means energy level 4 also has 7 f orbitals.

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Quick Trick

• Total number of orbitals for energy level n is
  n2.
• n 1 has 1 orbital (an s)
• n 2 has 4 orbitals (one s and 3 ps)
• n 3 has 9 orbitals (1 s, 3ps and 5ds)
• n 4 has 16 orbitals (1s, 3ps, 5ds and 7fs)

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Quantum Numbers

• Electron spin magnetic quantum number, ms,
  arbitrary designation thought to explain how 2
  electrons can be in same orbital
• Helps explain why some spectral lines are right
  together, but not in exactly the same frequency.
• 1/2 or -1/2 only fill in these two options
  under spin for each ml. (Most have been done for
  you.)

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Periodic Table Connection

• Lets label your table!!!! ?
• What are the 4 quantum numbers for the element
  C? K? Li?
• What element has the quantum numbers 1, 0, 0,
  -1/2?
• Practice WS

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Orbital Diagrams

• Orbital diagrams show the energy levels and
  orbitals of each electron in an atom
• Aufbau Principle
• Electrons occupy the lowest energy orbital
  possible.
• Fill lowest energy to highest.

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Pauli Exclusion Principle

• Wolfgang Pauli (1925)
• No two electrons in an atom can have the same
  set of four quantum numbers.
• No orbital may contain more than two electrons.
• Electrons in the same orbital must have opposite
  spin.

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• Recall that total number of orbitals for energy
  level n is n2.
• Two electrons per orbital max gives total number
  of electrons possible for that energy level as
  2n2.

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Atom Orbital Energies and Electron Assignments

• Electrons fill orbitals from lower energy to
  higher energy.
• n1 lt n2 lt n3 etc (generally)
• Energy sltpltdltf, (generally)
• More electrons in atom means more complex order.

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Hunds Rule

• Single electrons with the same spin must occupy
  each equal-energy orbital before additional
  electrons with opposite spins can be added.
• 1s 2s 2p
• (One in each box before pairing.)

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Orbital Diagrams

• Shows the arrangement of electrons in each
  orbital.
• Draw circles or boxes.
• Use a half arrow to indicate each electron ?.

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Examples

• Draw the orbital diagram for Li
• Li has 3 electrons
• 1s 2s
• N has 7 electrons
• 1s 2s 2p

http//intro.chem.okstate.edu/AP/2003SanAntonio/Wo
rkshopFolder/Electronconf.html
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Electron Configurations

• Show the arrangement of electrons
• Write the energy level number, the sublevel and
  number of electrons as a superscript.
• Ex. Li 3 electrons
• 1s2 2s1
• N 7 electrons
• 1s2 2s2 3p3

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Blocks on periodic table
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Can use noble gas configuration
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Write electron configurations for these

• A) Br
• C) Sb
• D) Re
• E) Tb
• F) Ti

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Answers

• A) Ar4s2 3d10 4p5
• B) Kr5s2
• C) Kr5s2 4d10 5p3
• D) Xe6s2 4f14 5d5
• E) Xe6s2 4f9
• F) Ar4s2 3d2

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• 19. 6
• 20. 11
• 21. Indium
• 22. Barium

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dfs Overlay Region

• What is electron configuration for potassium?
• Does it end in 3d1 or 4s1?
• Actually 4s is slightly lower energy than 3d.
• There is some overlay between subshells in higher
  energy levels.
• Aufbau mnemonic helps here. Still are exceptions.

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Atom Electron Configurations

• Review of Aufbau, use PT to write configurations,
  
• Know orbital diagrams, Hunds Rule
• Hunds Rule the most stable arrangement of
  electrons is that with the maximum number of
  unpaired electrons, (all with same spin
  direction).

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Some Exceptions Cr

• What would you expect the electron configuration
  for Cr to be?
• Ar 4s2 3d4 (expected from pattern)
• Actually, Ar 4s1 3d5
• This allows one electron in the s, and one in
  each of 5 d orbitals
• Some stability arises when orbitals are half-full.

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Some Exceptions Cu

• What would you expect the electron configuration
  for Cr to be?
• Ar 4s2 3d9 (expected from pattern)
• Actually, Ar 4s1 3d10
• This allows one electron in the s, and two in
  each of 5 d orbitals
• Why?

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Lanthanides

• Lanthanum Xe 6s2 5d1
• Cerium?
• Cerium Xe 4f16s2 5d1

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Ion Orbital Energies and Electron Configurations

• What is the electron configuration for a
  phosphide ion?
• Ne 3s2 3p3 for phosphorus atom
• phosphide is P-3, so 3 electrons are lost, so
  Ne 3s2

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What about metals with electrons in the dfs
overlay region?

• If an electron is removed from a 4th period
  transition metal, what happens?
• Recall the electrons fill 4s before 3d because of
  lower energy and repulsion between inner and
  outer electrons.
• When electrons are removed to form cations, the
  3d energy is lowered to a level below the 4s.

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All common transition metal cations have electron
configurations of noble gas core (n-1)dx.

• Think of first removing ns2 electrons, then the
  appropriate number of (n-1)d electrons.
• Fe Ar 3d6 4s2
• Fe2?
• Fe2 Ar 3d6
• Fe3
• Fe3 Ar 3d5
• Also, we know that ferrous ion is paramagnetic to
  the degree of 4 unpaired electrons, while the
  ferric ion is slightly more paramagnetic,
  reflective of 5 unpaired electrons.