Electron Clouds and Probability

I.     Rutherford-Bohr Atom
         1.  thought electrons orbit the nucleus
         2.  called the planetary model
         3.  atoms become excited when they absorb energy (exposed to light or other
              energy)
         4.  energy can be emitted or absorbed

          Terms
           spectroscopy:  study of substances exposed to some type of exciting energy
          spectrum:    pattern of radiant energy
          frequency:   number of waves peaks that occur in a unit of time
                                 symbol:  v
          hertz:  unit of frequency; one peak or cycle per second; Hz.
          speed of light:  3.00 x 108 m/s
                                      symbol:  c
          wavelength:  distance between two peaks or two troughs
                                   symbol:  h

                                        h= c/v

II.   Planck's Hypothesis
     1.  Quantum Theory
        a.  energy given off in quanta (little packets)
        b.  energy isn't continuous
      2.  Photons - quanta of radiant energy

                            E = hv

       E = one quanta of energy; J
       h = Planck's Constant; 6.6260755 x 10-34 J/Hz
       v = frequency; Hz

III.   The Hydrogen Atom & the Quantum Theory
        1.  Bohr - when an atom is excited, electrons can move from higher energy levels
                        to lower energy levels or vice versa.
        2.  higher to lower :  emits energy
             lower to higher:  absorbs energy
        3.  ground state:  energy level closest to the nucleus
        4.  Each element has its own unique atomic emission spectrum

            Light Emission
              a.  Atom absorbs energy
              b.  As a result, the electron is promoted from the ground state to an excited state
              c.  Eventually, the electron falls back down from the excited state to the ground state
              d.  When electron falls, it emits the same amount of energy that it absorbed before .
                    The energy is given off as light.

IV.   Modern Atomic Structure
      A.   de Broglie's Theory
            1.  proposed that electrons and other particles have both particle and
                 wave properties (1923)
            2.  proven correct two years later
      B.  Wave-Particle Duality of Nature
            -- All particles exhibit wave properties, and all waves exhibit particle
                properties.
      C.  Heisenburg
           1.  Chemists wanted to know th position and velocity of electrons.
                momentum = mass x velocity
           2.  Heisenburg Uncertainty Principle - it is impossible to know accurately
                both the position and the momentum of an electron at the same time.
                * measuring one quantity changes the other
      D.  Schrodinger
           1.  developed a mathematical equation that describes the behavior of the
                electron as a wave
           2.  solution of equation is used to calculate the probability of finding an
                electron at a particular point around the nucleus
      E.  Wave-Mechanical Model of the Atom
            1.  Bohr's model -- electrons orbit the nucleus in a specific path
            2.  Schrodinger's work led to the discovery of electron clouds
            3.  electron cloudvolume occupied by an electron; resembles turning fan
                                               blades that are 3-D

V.  Quantum Theory
     -- Each electron in an atom can be described by a unique set of four quantum
        numbers: n, l, m, and s.
     A.  Principle Quantum Number
          1.  n = 1, 2, 3, ....
          2.  the number of the energy level
          3.  describes the size of the electron cloud
          4.  energy increases as the size of the electron cloud increases
          5.  maximum number of electrons that can be contained in each level = 2n2
 
 

n
total # of e-
1
2
2
8
3
18
4
32
5
50
6
72
7
98

   B.  Energy Sublevels and Orbitals
       1.  l = 0...n-1
       2.  describes the shape of the electron cloud; shape is determined by the
            sublevels within the energy level
       3.  n = 4    then there are 4 sublevels:  4s, 4p, 4d, and 4f (in order of increasing
            energy)
       4.  4s and 3d overlap, so 3d has more energy than 4p
       5.  Orbitals
            a.  space occupied by one pair of electrons
            b.

sublevel
# of orbitals
s
1
p
3
d
5
f
7

  C.  Orientation of Orbitals
        1.  m = -l ...+l
        2.  describes orbitals orientation in space
        3.  degenerate orbitals:  have same energy, size, and shape.  They only differ in
             direction.
 D.  Distribution of Electrons
        1.  s = +/- 1/2
        2.  describes the spin direction of the electron, clockwise or counterclockwise

    Example:  Show how the four quantum numbers are used to describe the
                        electron structure of neon.
 
 

Electrons
n
l
m
s
1,2
1
0 (s)
0
+/- 1/2
3,4
2
0 (s)
0
+/- 1/2
5,6
2
1 (p)
-1
+/- 1/2
7,8
2
1 (p)
0
+/- 1/2
9,10
2
1 (p)
1
+/- 1/2

VI.  Electron Configurations
       -- way in which electrons are arranged around the nuclei of atoms
       A.  Rules that must be followed:
            1.  Aufbau Principle:  electrons enter orbitals of lowest energy first
            2.  Pauli Exclusion Principle:  no two electrons in an atom can have the
                 same set of quantum numbers
            3.  Hund's Rule:  when electrons occupy orbitals of equal energy, one
                 electron enters each orbital until all orbitals contain one electron with
                 parallel spin

      B.  Two Ways to Express Electron Configuration
            1.  Electron Energy Diagram

            2.  Line Notation

             Example:  Phosphorus, 15 electrons

                 electron configuration = 1s22s22p63s23p3

            3.  Short-hand Line Notation
            Example:  Mg, 12 electrons
            electron configuration = [Ne] 3s2

      C.  Lewis Electron Dot Diagrams
                  * used to show outer electrons
 

Element
electron configuration
Lewis Dot
H
1s1
H.
He
1s2
H:
O
1s22s22p4
.:
Cd
1s22s22p63s23p64s23d104p65s24d10
Cd: