Quantum Theory

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Quantum Theory
http//www.colby.edu/chemistry/CH141F/Chapter206
20presentation.ppt
Schrodinger
Heisenberg
http//staff.science.nus.edu.sg/PC1144/PC114420L
ectures/lecture16.ppt
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The Quantum Mechanical Model

• Energy is quantized. It comes in chunks.
• A quanta is the amount of energy needed to move
  from one energy level to another.
• Since the energy of an atom is never in between
  there must be a quantum leap in energy.
• Schrodinger derived an equation that described
  the energy and position of the electrons in an
  atom

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The Quantum Mechanical Model

• Heisenberg Uncertainty Principle---it is
  impossible to know both the exact position and
  momentum of an object at the same time.
• Cant know position if e- is moving.
• Cant know momentum if e- is not moving.

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The Quantum Mechanical Model

• Has energy levels for electrons.
• Orbits are not circular.
• It can only tell us the probability of finding
• an electron a certain distance from the nucleus.

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The Quantum Mechanical Model

• The atom is found inside a blurry electron
  cloud
• A area where there is a chance of finding an
  electron.
• Draw a line at 90

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Schrodingers Quantum s

• (n) Principal quantum
• n 1, 2, 3 ?-1
• the energy level of the electron.
• Formula 2(n)2 of electrons per energy level
• (l) Azimuthal or Secondary quantum
• l 0,1, 2, (n-1)
• the sublevels or shape within an energy level.
• s,p,d,f (names of sublevels)
• s,p,d, f each have a unique shape.

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Quantum s (cont.)

• (ml) magnetic quantum
• ml l .. 0 .. l (2l 1)
  total orbitals
• regions where there is a high probability of
  finding an electron
• each orbital can hold 2 e-
• (ms) spin quantum
• ms 1/2 or 1/2
• in each orbital there can be up to 2 electrons
  spinning in opposite directions.
• Clockwise ? 1/2 Counter clockwise ? 1/2

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Quantum Numbers
s
p
d
f
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Arrangement of Electrons in Atoms

• Electrons in atoms are arranged as
• LEVELS (n)
• SUBLEVELS (l)
• ORBITALS (ml)

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Energy Levels

• Each energy level has a number called the
  PRINCIPAL QUANTUM NUMBER, n
• Currently n can be 1 thru 7, because there are 7
  periods on the periodic table

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Energy Levels
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Orbitals and the Periodic Table

• Orbitals grouped in s, p, d, and f orbitals
• (sharp, proximal, diffuse, and fundamental)

s orbitals
d orbitals
p orbitals
f orbitals
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s orbitals

• 1 s orbital for every energy level
• Spherical shaped
• Each s orbital can hold 2 electrons
• Called the 1s, 2s, 3s, etc.. orbitals.

3s
2s
1s
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p orbitals

• Start at the second energy level
• 3 different directions
• 3 different shapes
• Each can hold 2 electrons

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d orbitals

• Start at the third energy level
• 5 different shapes
• Each can hold 2 electrons

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f orbitals

• Start at the fourth energy level
• Have seven different shapes
• 2 electrons per shape

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f orbitals
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Summary
of orbitals
Max electrons
Starts at energy level
s
1
2
1
p
3
6
2
5
10
3
d
7
14
4
f
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Number of Electrons that can be held in each
orbital

• s 2 e-
• p 6 e-
• d 10 e-
• f 14 e-

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Electron Configurations

• The way electrons are arranged in atoms.
• Aufbau principle- electrons enter the lowest
  energy first.
• This causes difficulties because of the overlap
  of orbitals of different energies.
• Pauli Exclusion Principle- at most 2 electrons
  per orbital - different spins
• Hunds Rule- When electrons occupy orbitals of
  equal energy they dont pair up until they have
  to .

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Electron Configuration

• Lets determine the electron configuration for
  Phosphorus (P)
• Need to account for 15 electrons

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• The first to electrons go into the 1s orbital
• Notice the opposite spins
• only 13 more

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• The next electrons go into the 2s orbital
• only 11 more

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• The next electrons go into the 2p orbital
• only 5 more

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• The next electrons go into the 3s orbital
• only 3 more

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• The last three electrons go into the 3p orbitals.
• They each go into seperate shapes
• 3 upaired electrons
• 1s22s22p63s23p3

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The easy way to remember

• 1s2

• 2 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2

• 4 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2

• 12 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2 3p6 4s2

• 20 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2

• 38 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2

• 56 electrons

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Fill from the bottom up following the arrows

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
  4f14 5d10 6p6 7s2

• 88 electrons

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Fill from the bottom up following the arrows
7s 7p 7d 7f
6s 6p 6d 6f

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
  4f14 5d10 6p6 7s2 5f14 6d10 7p6

5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s

• 108 electrons

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Effective Nuclear Charge

• Electrostatic repulsion between negatively
  charged electrons
• Influences the energies of the orbitals.
• The effect of repulsion is described as screening
  or shielding.
• The combined effect of attraction to the nucleus
  and repulsion from other electrons gives an
  effective nuclear charge, Zeff, which is less
  than that of the bare nucleus.

Zeff Z - S
Protons
Shielding electrons
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Periodicity of Effective Nuclear Charge
Z on valence electrons
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Effective Nuclear Charge, Zeff

• Atom Zeff Experienced by Electrons in Valence
  Orbitals
• Li 1
• Be 2
• B 3
• C 4
• N 5
• O 6
• F 7

Increase in Zeff across a period
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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.
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Electron Configurations

• 2p4

Number of electrons in the sublevel
Energy Level
Sublevel
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
4f14 etc.
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Lets Try It!

• Write the electron configuration for the
  following elements
• H
• Li
• N
• Ne
• K
• Zn
• Pb

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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

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Shorthand Notation

• Step 1 Find the closest noble gas to the atom
  (or ion), WITHOUT GOING OVER the number of
  electrons in the atom (or ion). Write the noble
  gas in brackets .
• Step 2 Find where to resume by finding the next
  energy level.
• Step 3 Resume the configuration until its
  finished.

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Shorthand Notation

• Chlorine
• Longhand is 1s2 2s2 2p6 3s2 3p5
• You can abbreviate the first 10 electrons with a
  noble gas, Neon. Ne replaces 1s2 2s2 2p6
• The next energy level after Neon is 3
• So you start at level 3 on the diagonal rule (all
  levels start with s) and finish the configuration
  by adding 7 more electrons to bring the total to
  17
• Ne 3s2 3p5

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Practice Shorthand Notation

• Write the shorthand notation for each of the
  following atoms
• Cl
• K
• Ca
• I
• Bi

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Valence Electrons

• Electrons are divided between core and valence
  electrons
• B 1s2 2s2 2p1
• Core He , valence 2s2 2p1

Br Ar 3d10 4s2 4p5 Core Ar 3d10 ,
valence 4s2 4p5
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Rules of the Game

• No. of valence electrons of a main group atom
  Group number (for A groups)

Atoms like to either empty or fill their
outermost level. Since the outer level contains
two s electrons and six p electrons (d f are
always in lower levels), the optimum number of
electrons is eight. This is called the octet
rule.
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Keep an Eye On Those Ions!

• Electrons are lost or gained like they always are
  with ions negative ions have gained electrons,
  positive ions have lost electrons
• The electrons that are lost or gained should be
  added/removed from the highest energy level (not
  the highest orbital in energy!)

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Keep an Eye On Those Ions!

• Tin
• Atom Kr 5s2 4d10 5p2
• Sn4 ion Kr 4d10
• Sn2 ion Kr 5s2 4d10
• Note that the electrons came out of the highest
  energy level, not the highest energy orbital!

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Keep an Eye On Those Ions!

• Bromine
• Atom Ar 4s2 3d10 4p5
• Br- ion Ar 4s2 3d10 4p6
• Note that the electrons went into the highest
  energy level, not the highest energy orbital!

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Try Some Ions!

• Write the longhand notation for these
• F-
• Li
• Mg2
• Write the shorthand notation for these
• Br-
• Ba2
• Al3

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Exceptions to Electron Configuration
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Exceptions to the Aufbau Principle

• Remember d and f orbitals require LARGE amounts
  of energy
• If we cant fill these sublevels, then the next
  best thing is to be HALF full (one electron in
  each orbital in the sublevel)
• There are many exceptions, but the most common
  ones are
• d4 and d9
• For the purposes of this class, we are going to
  assume that ALL atoms (or ions) that end in d4 or
  d9 are exceptions to the rule. This may or may
  not be true, it just depends on the atom.

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Exceptions to the Aufbau Principle

• d4 is one electron short of being HALF full
• In order to become more stable (require less
  energy), one of the closest s electrons will
  actually go into the d, making it d5 instead of
  d4.
• For example Cr would be Ar 4s2 3d4, but since
  this ends exactly with a d4 it is an exception to
  the rule. Thus, Cr should be Ar 4s1 3d5.
• Procedure Find the closest s orbital. Steal one
  electron from it, and add it to the d.

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Exceptions to the Aufbau Principle

• OK, so this helps the d, but what about the poor
  s orbital that loses an electron?
• Remember, half full is good and when an s loses
  1, it too becomes half full!
• So having the s half full and the d half full is
  usually lower in energy than having the s full
  and the d to have one empty orbital.

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Exceptions to the Aufbau Principle

• d9 is one electron short of being full
• Just like d4, one of the closest s electrons will
  go into the d, this time making it d10 instead of
  d9.
• For example Au would be Xe 6s2 4f14 5d9, but
  since this ends exactly with a d9 it is an
  exception to the rule. Thus, Au should be Xe
  6s1 4f14 5d10.
• Procedure Same as before! Find the closest s
  orbital. Steal one electron from it, and add it
  to the d.

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Orbitals fill in order

• Lowest energy to higher energy.
• Adding electrons can change the energy of the
  orbital.
• Half filled orbitals have a lower energy.
• Makes them more stable.
• Changes the filling order

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Write these electron configurations

• Titanium(Ti) - 22 electrons
• 1s22s22p63s23p64s23d2
• Vanadium(V) - 23 electrons 1s22s22p63s23p64s23d3
• Chromium(Cr) - 24 electrons
• 1s22s22p63s23p64s23d4 is expected
• But this is wrong!!

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Chromium is actually

• 1s22s22p63s23p64s13d5
• Why?
• This gives us two half filled orbitals.
• Slightly lower in energy.
• The same principal applies to copper.

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Coppers electron configuration

• Copper has 29 electrons so we expect
• 1s22s22p63s23p64s23d9
• But the actual configuration is
• 1s22s22p63s23p64s13d10
• This gives one filled orbital and one half filled
  orbital.
• Remember these exceptions

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