THE ELECTRON

							The Electron
    Part 2
The Quantum Model of the Atom
• In 1927, Werner Heisenberg
  proposed his uncertainty principle.
  – You can’t know both the velocity &
    position of a particle at the same time
  – Meaning we can’t predict
    the exact location of an e-
    or it’s path in the atom
  – Whatever you use to
    measure the location of
    an electron will cause the
    electron to move
To detect the position of an electron you might use a photon.
Unfortunately, when the photon collides with the electron the
force of the collision causes the electron to change position,
     so the best you can tell is where the electron was.
The Quantum Model of the Atom
• The biggest effect of the Uncertainty
  Principle on Bohr’s model is that
  there is no way to define the path of
  the e- around its nucleus with any
  accuracy.
  – The best we can do is make an educ-
    ated guess within a certain range of
    probability that the e- is in a particular
    region around the nucleus.
The Quantum Model of the Atom
• In 1926, the physicist Erwin Schrod-
  inger took the atom 1 step further.
  – He proposed a mathematical
    equation to describe the location &
    energy of the e- in a H atom.
  – He used calculated the “wave func-
    tion” of the e-, or the probability of
    locating the e- a certain distance from
    the nucleus
    • the quantum mechanical model is
      based on Schrodinger’s work.
The Quantum Model of the Atom
The Quantum Model of the Atom
• Like the Bohr model, the quantum
  mech model of the atom restricts the
  energy of e-’s to quantized values.
  – But, the quantum mechanical model
    doesn’t define a specific path an elec-
    tron takes around the nucleus.
    • Instead it estimates the probability of
      finding an electron in a certain
      position.
                        Bohr’s model gave
                       the e- specific paths
                       around the nucleus,
                       based on the energy
                          of the electron




 However, we can only
 guess within a certain
degree of probability the
    location of an e-
The Quantum Model of the Atom
• The probability of finding an electron
  within a certain volume of space
  surrounding the nucleus can be
  represented by a fuzzy cloud
  – The cloud is more dense
    where the probability of
    finding the e- is higher.
The Quantum Model of the Atom
• Each electron in a given atom is
  given a set of 4 values called
  quantum numbers, that describe an
  electron’s behavior.
  – The 1st 3 quantum numbers map the
    electron’s location, the 4th describes
    the electron’s orientation.
  – No 2 electrons have an identical set
    of four quantum numbers.
The Quantum Model of the Atom
• You can assign every electron in a
  given atom (element) a set of 4 quan-
  tum numbers
• The quantum numbers act as the
  electron’s address in the atom.
• Quantum #’s can be described as a
  kind of coordinate system to map the
  location of an e- in the atom.
The Quantum Model of the Atom
• The problem with e- in the atom is
  that they can’t be pinned down to a
  precise location because of Heisen-
  berg’s Uncertainty Principle
  – So the quantum #’s only give a fuzzy
    or probable location of the electron in
    the atom.
The Quantum Model of the Atom
• An analogy of quantum numbers
  might help.
 – We can think about the quantum #’s
   as perhaps like trying
   to find our seat in
   Rupp Arena
   using a ticket stub.
The Quantum Model of the Atom
• Each piece of information on your
  ticket stub gets you closer and closer
  to your seat.
  – Each quantum number gets us closer
    and closer to the probable location of
    an electron
The Quantum Model of the Atom
• The 1st quantum number is the
  “Principle Quantum Number”
  – symbolized by n.
  – can values of 1 to infinity.
• The larger the value of n, the farther
  from the nucleus the electron is.
  – These electrons are more energetic
    so the volume of their appearance is
    larger
The Quantum Model of the Atom
• Each energy level has a limit to the
  number of electrons it can hold.
  –   n=1 can hold 2 electrons
  –   n=2 can hold 8 electrons
  –   n=3 can hold 8 electrons
  –   n=4 can hold 18 electrons
  –   n=5 can hold 18 electrons
  –   n=6 can hold 32 electrons
The Quantum Model of the Atom
• The Principle quantum number can
  be compared to the level of Rupp.
  – The Upper Arena is farther from the
    floor than the Lower Arena
  – The larger the principal quantum
    number the farther from the nucleus.
The Quantum Model of the Atom
• The 2nd Quantum number is the
  “Azimuthal Quantum number”
  – Symbolized with an “l,”
  – can have numbers of 0, 1, 2, 3 which
    correspond to the letters s, p, d, f.
  – indicates a shape of an orbital
  – “l” is expressed with letters rather
    than numbers.
    • An s orbital is spherical
    • A p orbital is dumb-bell
    • A d is mostly clover-leaf
    • An f is really complicated
The Quantum Model of the Atom
• Each l is called an orbital
  – An orbital is the region or volume
    around the nucleus of an atom where
    an electron with a given energy is
    likely to be found.
The Quantum Model of the Atom
• Every energy level (quantum # - n)
  contains 1 and only 1 s sublevel
  – The number of sublevels in any given
    n is theoretically related to the value
    of n
    • n=1has 1 sublevel…only the s
    • n=2 has 2 sublevels…s & p
    • n=3 has 3 sublevels…s, p, & d
    • n=4 has 4 sublevels…s, p, d, & f
The Quantum Model of the Atom
• The quantum # l might correspond to
  the section number on our stub
  – It narrows down for us to the specific
    area in the upper arena that our seat
    is in.
  – The l quantum number gives us the
    sublevel of the electron on the energy
    level.
The Quantum Model of the Atom
• The 3rd Quantum number is the
  “Orientation/Orbital quantum
  number”
  – Symbolized by ml
  – Within each sublevel, are orbitals –
    each with a different orientation.
  – Each orbital higher than ml = 1 can
    have a different orientation on the
    Cartesian axis (x, y, & z)
The Quantum Model of the Atom
• On a map ml might be thought of as
  the row our seat is located on.
  – The row narrows down for us where
    in the section our seat is.
  – In the atom, ml gives the direction that
    the shape of the volume that the
    electron occupies points.
The Quantum Model of the Atom
• Together the l and ml quantum
  numbers give valuable info about the
  electrons probable location
• The “s” sublevel (l =0; ml = 0):
  – Spherical shape and only one
    allowed in each energy level.
  – As the energy increases (n) the “s”
    orbital also gets bigger.
The Quantum Model of the Atom
• The p-sublevel: (l =1; ml=-1,0, or 1)
  – Shaped like a dumbbell.
  – There are 3 orbitals designated px, py,
    or pz in each energy level. (Based on
    axis on the cartesian coordinates)
  – The p orbitals are higher energy then
    s orbitals
  – Only found in ground state atoms
    containing 5 electrons or more
The Quantum Model of the Atom
• The d-orbital (l =2; ml= -2, -1, 0, 1, 2):
  – The d orbitals have more
    complicated shapes.
  – There are 5-d orbitals in each energy
    level that they appear.
  – The d-orbitals appear only after the
    2nd energy level, and beyond
  Proposed
  composite
of 5 d-orbitals
The Quantum Model of the Atom
• The f-orbital
  (l = 3; ml = -3, -2, -1, 0, 1, 2, 3)
  – Most energetic and complicated
  – There can be 7 “f” orbitals for each
    energy level that they occupy.
The Quantum Model of the Atom
• There is a limit to how many electrons
  that each sublevel can hold, which
  limits the number of electrons that
  can have the same relative energy
    Sublevel    # of      Maximum #
               Orbitals   of Electrons
        s         1             2
        p         3             6
        d         5            10
        f         7            14
The Quantum Model of the Atom
• The 4th and final Quantum Number,
  is the Spin quantum number
  – Symbolized by ms
  – Each orbital can hold at most 2
    electrons,
    • They must spin in opposite directions
      on their axes designated (+½ & -½)
The Quantum Model of the Atom
• The spin quantum number might
  work somewhat like the seat number
  on the ticket stub.
  – There is only one possible seat that
    corresponds to the information on
    your ticket.
  – There is only one possible electron
    that matches a given set
    of quantum numbers
The Quantum Model of the Atom
Set of (n, l, ml, ms)
• H only has 1 electron, and it is on the
  n=1 energy level, and it’s in the s-
  sublevel
  – (1,0,0,+½)
• He has 2 electrons, and they are both
  on the n=1 energy level, and in the s
  sublevel
  – (1,0,0,+½)(1,0,0,-½)
The Quantum Model of the Atom
• Lithium has an electron in the n=2
  energy level and so on….
  – 3Li: (1,0,0,+½) (1,0,0,-½)
         (2,0,0,+½)
  – 4Be: (1,0,0,+½) (1,0,0,-½)
         (2,0,0,+½) (2,0,0,-½)
  – 5B: (1,0,0,+½) (1,0,0,-½)
         (2,0,0,+½) (2,0,0,-½)
         (2,1,-1,+½)
The Quantum Model of the Atom
• Continuing With n=2
  – 6C: (1,0,0,+½) (1,0,0,-½)
        (2,0,0,+½) (2,0,0,-½)
        (2,1,-1,+½) (2,1,0,+½)
  – 7N: (1,0,0,+½) (1,0,0,-½)
        (2,0,0,+½) (2,0,0,-½)
        (2,1,-1,+½) (2,1,0,+½)
        (2,1,1,+½)
The Quantum Model of the Atom
 – 8O: (1,0,0,+½) (1,0,0,-½)
       (2,0,0,+½) (2,0,0,-½)
       (2,1,-1,+½) (2,1,0,+½)
       (2,1,1,+½) (2,1,-1,-½)
 – 9F: (1,0,0,+½) (1,0,0,-½)
       (2,0,0,+½) (2,0,0,-½)
       (2,1,-1,+½) (2,1,0,+½)
       (2,1,1,+½) (2,1,-1,-½)
       (2,1, 0,-½)
The Quantum Model of the Atom
 –   10Ne:   (1,0,0,+½) (1,0,0,-½)
             (2,0,0,+½) (2,0,0,-½)
             (2,1,-1,+½) (2,1,0,+½)
                (2,1,1,+½) (2,1,-1,-½)
             (2,1, 0,-½) (2,1,1,-½)
Not every orbital
is found in every
   energy level.
(ie.The n=1 level
   only contains
  the s orbital)
Electron Configurations
• The distribution of electrons among
  the energy levels, sublevels,
  orientations, and spins of an atom is
  known as the electron configuration.
  – Having a basic understanding of how
    the electrons are configured helps us
    determine the interaction of atoms of
    elements to other elements
  – When they come into contact it’s the
    outer electrons that do the chemistry.
Electron Configurations
• Electron configurations are determin-
  ed by distributing electrons among
  levels, sublevels, & orbitals, in order
  of lowest in energy to highest.
• We can predict the location of the
  electrons in the atoms by following 3
  important principles:
Electron Configurations
• The Aufbau Principle
  – Electrons are added one at a time to
    the lowest energy orbitals available
    until all electrons are distributed.
  – The # of electrons distributed,
    depends on the atomic # of the atom.
  – We’ll use a diagram to help
    placement in the proper order
Electron Configurations
• The Pauli Exclusion Principle
  – An orbital can hold a maximum of
    2 electrons.
  – To occupy the same orbital the
    electrons must spin in opposite
    directions.
     • Depicted with arrows         orbital
       pointed in opposite
       directions.

                           2 electrons
Electron Configurations
• Hund’s Rule
  – Electrons occupying equal-energy
    orbitals, are distributed so that the
    maximum number of unpaired
    electrons results.
  – For ex, with Nitrogen’s 7 electrons
       1        2             2
       s        s             p
                   4d
         5s
              4p
                   3d
Energy


         4s
              3p

                        Oxygen
         3s
              2p
         2s


         1s
                   4d
         5s
              4p
                   3d
Energy


         4s
              3p

                        Nickel
         3s
              2p
         2s


         1s
Electron Configurations
• We generally don’t draw the energy
  pattern and then fill in the boxes for
  the configurations. We generally use
  this type of notation:
                      # of electrons
 Principal            in the orbital
 Energy
 Level

       Orbital Type
Electron Configurations
• We generally don’t draw the energy
  pattern and then fill in the boxes for
  the configurations. We generally use
  this type of notation:
                      # of electrons
 Principal            in the orbital
 Energy
 Level

       Orbital Type
Electron Configurations
• We generally don’t draw the energy
  pattern and then fill in the boxes for
  the configurations. We generally use
  this type of notation:
                        # of electrons
 Principal              in the orbital
 Energy
 Level

       Orbital Type
Electron Configurations
• We generally don’t draw the energy
  pattern and then fill in the boxes for
  the configurations. We generally use
  this type of notation:
                        # of electrons
 Principal              in the orbital
 Energy
 Level

       Orbital Type
Electron Configurations
• We generally don’t draw the energy
  pattern and then fill in the boxes for
  the configurations. We generally use
  this type of notation:
                             # of electrons
 Principal                   in the orbital
 Energy
 Level

       Orbital Type
Electron Configurations
• To help write the electron configura-
  tions we can use one of two tools.
• You choose the one that is most
  comfortable for you.
  – The periodic table
  – The Aufbau diagram hanging in the
    room
Electron Configurations
• Fe (Atomic Number = 26)
  1s2 2s2 2p6 3s2 3p6 4s2 3d6
• Mg (Atomic Number = 12)
  1s2 2s2 2p6 3s2
• Ne (Atomic Number = 10)
  1s2 2s2 2p6
• Ti (Atomic Number = 22)
  1s2 2s2 2p6 3s2 3p6 4s2 3d2
• Zr (Atomic Number=40)
  1s2 2s2 2p6 3s2 3p64s2 3d10 4p6 5s2 4d2
Electron Configurations
• Don’t have to write out the entire
  electron configuration.
• There is a short-cut:
  – Keeps focus on valence electrons
  – An atom’s inner electrons are
    represented by the symbol for the
    nearest noble gas with a lower atomic
    number.
                             K: [Ar]4s1
Electron Configurations

    For the element Phosphorus
           -- 15 electrons
          1s22s22p63s23p3

            P:   [Ne] 3s 23p3
                            MUST BE A
                            NOBLE GAS
Electron Configurations
Let’s do a couple more:
       Ba: [Xe]   6s 2

       Hg: [Xe] 6s2 4f14 5d10
        V: [Ar] 4s2 3d3
Exceptions to the order of filling
Electron Configurations
• The chemistry of an atom occurs at
  the set of electrons called valence
  electrons
• The valence electrons are the outer-
  most s and p electrons of the atom.
  – 2 s electrons + 6 p electrons = a full
    set of valence electrons
• The arrangement of the valence e-
  lead to the elements properties.