Chapter 7 The Quantum-Mechanical Model of the Atom by phf13063

VIEWS: 321 PAGES: 63

									             Chapter 7
      The Quantum-Mechanical
         Model of the Atom

Read/Study: Chapter 7 in your textbook!
Study/Master: Class Lecture Notes
MGC Assignments: Due April 4 at 11:50 pm
MGC Quiz for Chapter 7: Quiz AFTER Chapter 9!

Massive Brain Power – Solvay Conference 1927

Definition of Chemistry:
  The study of the properties, composition, and
  STRUCTURE of matter, the physical and
  chemical changes it undergoes, and the energy
  liberated or absorbed during those changes.

The foundation for the STRUCTURE of inorganic
materials is found in the STRUCTURE of the atom.
                Material Properties

                   Bulk Structure

                 Molecular Structure

                  Atomic Structure                 3
  Historical Development:
    Greek Concepts of Matter

       Aristotle - Matter is continuous, infinitely
       divisible, and is composed of only 4 elements:
          Earth, Air, Fire, and Water

        Won the philosophical/political battle.
        Dominated Western Thought for Centuries.
        Seemed very “logical”.
        Was totally WRONG!!

Review Chapter 2 Discussions!
The “Atomists” (Democritus, Lucippus,
Epicurus, et. al.) - Matter consists ultimately
of “indivisible” particles called “atomos” that
canNOT be further subdivided or simplified.
If these “atoms” had space between them,
nothing was in that space - the “void”.

 Lost the philosophical/political battle.
 Lost to Western Thought until 1417.
 Incapable of being tested or verified.
 Believed the “four elements” consisted of
 “transmutable” atoms.
 Was a far more accurate, though quite imperfect
 “picture” of reality.
Modern Concepts of Matter
John Dalton (1803) - An atomist who formalized
the idea of the atom into a viable scientific theory
in order to explain a large amount of empirical
data that could not be explained otherwise.

 Matter is composed of small “indivisible” particles
 called “atoms”.
 The atoms of each element are identical to each
 other in mass but different from the atoms of other
 A compound contains atoms of two or more
  elements bound together in fixed proportions
  by mass.                                              6
 A chemical reaction involves a rearrangement of
  of atoms but atoms are not created nor destroyed
  during such reactions.

Present Concepts - An atom is an electrically
neutral entity consisting of negatively charged
electrons (e-) situated outside of a dense, posi-
tively charged nucleus consisting of positively
charged protons (p+) and neutral neutrons (n0).

     Particle    Charge Mass
     Electron     -1    9.109 x 10 -28 g
     Proton       +1    1.673 x 10 -24 g
     Neutron       0    1.675 x 10 -24 g
Model of a
Helium-4          e-     no p+      e-
(4He) atom

                                         Electron Cloud

How did we get this concept? - This portion of our
program is brought to you by:
Democritus, Dalton, Thompson, Planck, Einstein, Millikan,
Rutherford, Bohr, de Broglie, Heisenberg, Schrödinger,
Chadwick, and many others.           CHRISTMAS
  Democritus - First atomic ideas
  Dalton - 1803 - First Atomic Theory
  J. J. Thompson - 1890s - Measured the charge/mass
      ratio of the electron (Cathode Rays)

         _                                     Material

                   Anode      Electric Field
                              Source (Off)

With the electric field off, the cathode ray is not deflected.
                                  -            Fluorescent
           -                                   Material
                    +             +
                  Anode    Electric Field
                           Source (On)

With the electric field on, the cathode ray is deflected
away from the negative plate. The stronger the electric
field, the greater the amount of deflection.

               Anode                  Magnet
With the magnetic field present, the cathode ray is
deflected out of the magnetic field. The stronger the
magnetic field, the greater the amount of deflection.

                 e/m = E/H2r
e = the charge on the electron
m = the mass of the electron
E = the electric field strength
H = the magnetic field strength
r = the radius of curvature of the electron beam

Thompson, thus, measured the charge/mass ratio
of the electron - 1.759 x 108 C/g
Summary of Thompson’s Findings:

 Cathode rays had the same properties no matter
 what metal was being used.

 Cathode rays appeared to be a constituent of all
 matter and, thus, appeared to be a “sub-atomic”

 Cathode rays had a negative charge.

 Cathode rays have a charge-to-mass ratio
 of 1.7588 x 108 C/g.

   R. A. Millikan - Measured the charge of the electron.
   In his famous “oil-drop” experiment, Millikan was able to
   determine the charge on the electron independently of its
   mass. Then using Thompson’s charge-to-mass ratio, he
   was able to calculate the mass of the electron.

e = 1.602 10 x 10-19 coulomb
e/m = 1.7588 x 108 coulomb/gram
m = 9.1091 x 10-28 gram

 Goldstein - Conducted “positive” ray experiments that
 lead to the identification of the proton. The charge
 was found to be identical to that of the electron and
 the mass was found to be 1.6726 x 10-24 g.
              ATOMIC STRUCTURE
     Ernest Rutherford - Developed the “nuclear” model
     of the atom.
          The Plum Pudding Model of the atom:
                                 A smeared out “pudding”
                                 of positive charge with
                                 negative electron “plums”
                                 imbedded in it.

          The Metal Foil Experiments:
Radioactive     a-particles                  Screen
Material in
Pb box.
If the plum pudding model is correct, then all of
the massive a-particles should pass right through
without being deflected.

In fact, most of the a - particles DID pass right
through. However, a few of them were deflected at
high angles, disproving the “plum pudding” model.

Rutherford concluded from this that the atom con-
sisted of a very dense nucleus containing all of the
positive charge and most of the mass surrounded
electrons that orbited around the nucleus much as
the planets orbit around the sun.
Problems with the Rutherford Model:

It was known from experiment and electromagnetic
theory that when charges are accelerated, they
continuously emit radiation, i.e., they loose energy
continuously. The “orbiting” electrons in the atom
were, obviously, not doing this.

       Atomic spectra and blackbody radiation
        were known to be DIScontinuous.

       The atoms were NOT collapsing.

      Atomic Spectra - Since the 19th century, it had
      been known that when elements are heated until
      they emit light (glow) they emit that light only at
      discrete frequencies, giving a line spectrum.


Gas                                         Line Spectrum

Emission Spectra

Absorption Spectra

  When white light is passed through a sample of
  the vapor of an element, only discrete frequencies
  are absorbed, giving a absorption ban spectrum.
  These frequencies are identical to those of the
  line spectrum of the same element.

 For hydrogen, the spectroscopists of the 19th
 Century found that the lines were related by the
 Rydberg equation:

                n/c = R[(1/m2) - (1/n2)]
n = frequency                R = Rydberg Constant
c = speed of light           m = 1, 2, 3, ….
                     n = (m+1), (m+2), (m+3), ….       19
Max Planck - In 1900 he was investigating the nature
of black body radiation and tried to interpret his
findings using accepted theories of electromagnetic
radiation (light). He was NOT successful since these
theories were based on the assumption that light had
WAVE characteristics.

To solve the problem he postulated that light was
emitted from black bodies in discrete packets he
called “quanta”. Einstein later called them
“photons”. By assuming that the atoms of the black
body emitted energy only at discrete frequencies, he
was able to explain black body radiation.

                  E = hn = hn/l                        20
Photoelectric Effect!  Ever checked out of a
grocery store? Ever walked into or out of a
Grocery store? Ever physically opened a
door at the grocery store?
Both spectroscopy and black body radiation
indicated that atoms emitted energy only at
discrete frequencies or energies rather than

  Is light a particle or a wave??

  Why do atoms emit only discrete energies?

  What actually happens when light interacts
  with matter?

  What was wrong with Rutherford’s Model?

Niels Bohr - Bohr corrected Rutherford’s model
of the atom by formulating the following postulates:

 Electrons in atoms move only in discrete orbits
around the nucleus.
 When in an orbit, the electron does NOT emit
 They may move from one orbit to another but are
NEVER residing in between orbits.
 When an electron moves from one orbit to
another, it absorbs or emits a photon of light with a
specific energy that depends on the distance between
the two orbits.

Paschen                  +                 (UV)

             The Bohr Model of the Atom

 The lowest possible energy state for an electron
is called the GROUND STATE. All other states
are called EXCITED STATES.

        En = (- 2.179 x 10-18 J)/n2

           Ephoton = Efinal - Einitial

Ephoton = [(- 2.179 x 10-18 J)/n2final]
          -[(- 2.179 x 10-18 J)/n2initial]
        = - 2.179 x 10-18 J[(1/n2final) - (1/n2initial)]
          Does this equation look familiar?
              n/c = R[(1/m2) - (1/n2)]
Niels Bohr won the Nobel Prize for his work.
However, the model only worked perfectly for
hydrogen. What about all of those other elements??

Louis de Broglie - Thought that if light, which was
thought to have wave characteristics, could also have
particle characteristics, then perhaps electrons, which
were thought to be particles, could have characteristics
of waves.

    l = h/mv where “mv” is momentum

An electron in an atom was a “standing wave”!

Werner Heisenberg - Developed the “uncertainty”
principle: It is impossible to make simultaneous and
exact measurements of both the position (location)
and the momentum of a sub-atomic particle such as
an electron.

            (Dx)(Dp) > h/2p

Our knowledge of the inner workings of atoms and
molecules must be based on probabilities rather
than on absolute certainties.
Erwin Schödinger - Developed a form of quantum
mechanics known as “Wave Mechanics”.

Wave Function - A mathematical function associated
with each possible state of an electron in an atom or

    It can be used to calculate the energy of an
   electron in the state

    the average and most probable distance from the

    the probability of finding the electron in any
   specified region of space.

Quantum Numbers:
    Principle Quantum Number, n - An integer
    greater than zero that represents the principle
    energy level or “shell” that an electron occupies.

              Energy                   # of orbitals
n             Level        Shell              n2
1              1st          K                 1
2              2nd          L                 4
3              3rd          M                 9
4              4th          N                16
etc.           etc.         etc.             etc.

Azimuthal Quantum Number, l - The quantum
number that designates the “subshell” an electron
occupies. It is an indicator of the shape of an orbital
in the subshell. It has integer values from 0 to n-1.
             l = 0, 1, 2, 3, 4, …, n - 1
                s p d f g….
Magnetic Quantum Number, ml - The quantum
number that determines the behavior of an electron
in a magnetic field. It has integer values from -l to
+l including 0.
        ml = -l, …, -3, -2, -1, 0, +1, +2, +3, …, +l

              Orbital                       # of
n      l      Name              ml         Orbitals
1      0       1s                0             1
2      0       2s                0             1
       1        2p           -1, 0, +1         3
3      0       3s                0             1
       1        3p           -1, 0, +1         3
       2       3d        -2, -1, 0, +1, +2     5
etc.   etc.    etc.             etc.          etc.

Spin Quantum Number, ms - The quantum number
that designates the orientation of an electron in a
magnetic field. It has half-integer values, +½ or -½.
So what do atoms look like?
A. Interpretation of Y: The probability of finding
an electron in a small volume of space centered
around some point is proportional to the value of
Y2 at that point.
B. Electron Probability Density vs. r

C. Dot Density Representation: Imagine super-
imposing millions of photographs taken of an
electron in rapid succession.

D. Radial Densities
        Quantum Numbers

5   0              0        One 5s Orbitals
    1          +1, 0, -1   Three 5p Orbitals
               Chapter 8
   Periodic Properties of the Elements

Read/Study: Chapter 8 in e-Textbook!

Study/Master: Class Lecture Notes

MGC Assignments: Due April 9 at 11:50 pm

MGC Quiz after Chapter 9: Not yet prepared!

Electron Configuration

  A. Many-electron atom: An atom that contains
  two or more electrons.

  B. Problems with the Bohr model:

     1. It “assumed” quantization of the energy
     levels in hydrogen.

     2. It failed to describe or predict the spectra
     of more complicated atoms.

C. What are the differences in electron energy
levels in hydrogen vs. more complicated atoms?

    3s          3p                    3d

    2s          2p

               Ground State Hydrogen Atom

     Splitting of the Degeneracy

2s      2p

H                           Li
      Splitting of the Degeneracy

1. In hydrogen, all subshells and orbitals in a
given principal energy level have the same energy.
They are said to be Degenerate.

2. In many-electron atoms, s-orbitals have lower
energy than p-orbitals which have lower energy
than d-orbitals which have lower energy than
f-orbitals, etc., etc.

3. Reason: Complex electrostatic interactions.

                    -        -       -             -
 Hydrogen                                  +++

                   Helium                Lithium

A. Shielding Effect - A decrease in the nuclear force
of attraction for an electron caused by the presence
of other electrons in underlying orbitals.

B. Effective Nuclear Charge - A positive charge
that may be less than the atomic number. It is the
charge “felt” by outer electrons due to shielding by
electrons in underlying orbitals.
The Pauli Exclusion Principle - No two electron in
the same atom can have the same four quantum

           H + e-  H -

Quantum           Electron 1        Electron 2
  n                     1                 1
  l                     0                 0
  ml                    0                 0
  ms                  +1/2              -1/2

The Aufbau Principle - A procedure for “building up”
the electronic configuration of many-electron atoms
wherein each electron is added consecutively to the
lowest energy orbital available, taking into account
the Pauli exclusion principle.

Order of Filling -
1s   2s     2p     3s   3p   4s    3d   4p    5s

  1s           Increasing Energy
  2s   2p
  3s   3p 3d
  4s   4p 4d 4f
  5s   5p 5d 5f 5g
Designating Electron Configurations -

 Standard Designation
   H     1s1    Li    1s2 2s1          B   1s2 2s2 2p1

   He    1s2    Be    1s2   2s2        C   1s2 2s2 2p2

 Orbital Diagram Designation

   H                 Li                B
        1s                1s      2s       1s 2s     2p
   He                Be                C
        1s                1s      2s       1s 2s     2p

 Core Designation - A designation of electronic
configuration wherein the outer shell electrons
are shown along with the “core” configuration of
the closest previous noble gas.
  Li   [He] 2s1               Be    [He] 2s2

  Na [Ne] 3s1                 Mg    [Ne] 3s2

  K    [Ar] 4s1               Ca    [Ar] 4s2
  Rb                          Sr
       [Kr] 5s1                     [Kr] 5s2

Hund’s Rule of Maximum Multiplicity - Electrons
occupy a given subshell singly and with parallel spins
until each orbital in the subshell has one electron.

   “Electrons try to stay as far apart as possible”

 Elevator Analogy            Bus Seat Analogy

B [He] 2s2 2p1      [He]

C [He] 2s2 2p2      [He]

N [He] 2s2 2p3      [He]
                           2s        2p
The Structure of the Periodic Table

 Historical Development - Dimitri Mendeleev and
Lothar Meyer independently found that when the
elements are ordered according to their atomic masses,
similar properties recur periodically. Were they right?

 The Periodic Law - The properties of the elements
are periodic functions of their atomic number.

 Physical Structure of the Table

Electronic Configuration and the Periodic Table

 s-Block Elements
 p-Block Elements
 d-Block Elements
 f-Block Elements

Assignment: Write the electron configuration using
all three types of designation for lead (Pb).

Electronic Configuration for positive ions (cations) -
Cations are formed by removing electrons in order
of decreasing n value. Electrons with the same n
value are removed in order of decreasing l value.
Electronic Configuration and the Periodic Table

 s-Block Elements
 p-Block Elements
 d-Block Elements
 f-Block Elements

Assignment: Write the electron configuration using
all three types of designation for lead (Pb).

Pb 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14
  5d10 6p2

Pb [Xe] 6s2 4f14 5d10 6p2 (You do the orbital diagram
The properties of the elements are determined in
large measure by their Atomic Number and their
Electron Configuration.

 Paramagnetism - A property that arises from
  unpaired electrons in an atom or molecule. It
  is identified by the fact that when the element
  is placed in a magnetic field in a magnetic
  susceptibility experiment, the atom or molecule
  is drawn into the field.

Assignment: Name the elements of the first 40
elements in the Periodic Table that are diamagnetic.

       Atomic Size -
        Atomic radii are considered to be 1/2 of the
        average distance between centers of identical
        atoms that are touching each other. This will
        vary with the chemical environment the atom
        is in.
pm                          Fluorine


  C - 77 pm                F - 71 pm

Trends in Atomic Radii:
1. Atomic radii increase from top to bottom in a
   family or group.

   The number of electrons and the nuclear
   charge are increasing! - Tends to shrink atom.

   But extra electron are added to new shells that
   are further from the nucleus and more
   effectively shielded from the nucleus - Tends to
   make the atom larger.

2. Atomic radii decrease from left to right
   across a row or period.

   The number of electrons and the nuclear
   charge are increasing! - Tends to shrink atom.

   The electrons are being added to the same
   shell and are not well shielded and thus, the
   atoms get smaller.

3. Summary of trends

   Down a Group - Larger
   Across a Period - Smaller
    What Affects Atomic/Ionic Sizes?

 The Charge on the Nucleus

 Shielding - This reduces the actual nuclear
 charge resulting in an “effective” nuclear

4. Some Exceptions

   Al - Ga

   The Lanthanide Contraction

 Ionic Size -

Based on the internuclear distance of cations and
anions in ionic crystals.

Not easy to determine how to apportion this
distance between the cation and the anion.

Cations - Monatomic cations are smaller than
their parent atoms.

   The whole outer shell is typically removed.

   The effective nuclear charge is increased.

 Na atom           Na+ ion
 186 nm            102 nm

 Anions - Monatomic anions are larger than
 their parent atoms.

     The extra electrons are typically added to
      the same shell where they are repelled by
      the other electrons already present, making
      the ion bigger than its parent atom.

F Atom         Fluoride Ion
71 nm            136 nm

 Ionization Energy - The energy required to
  remove an electron from a gaseous ground-
  state atom or ion.

  A. First Ionization Energy - The energy
     required to remove the most loosely bound
     electron from the valence shell.

  B. Second Ionization Energy - The energy
     required to remove the second electron
     after the first one is gone.

  C. Third Ionization Energy - Etc., Etc., Etc.

Li (g)   Li+   +   e-    IE1 = +520 kJ/mol

Li+      Li2+ +    e-    IE2 = +7298 kJ/mol

Na (g)   Na+   +   e-    IE1 = +496 kJ/mol

Na+      Na2+ +     e-   IE2 = +4564 kJ/mol

Na2+     Na3+ +     e-   IE3 = +6918 kJ/mol

Mg (g)   Mg+   +   e-    IE1 = +737 kJ/mol

Mg+      Mg2+ +    e-    IE2 = +1447 kJ/mol

Mg2+     Mg3+ +    e-    IE3 = +7738 kJ/mol
  Electron Affinity - The energy absorbed when
   an electron is added to a gaseous ground-state
   atom or ion. It has the same sign as the D H of
   the process.

    Cl (g) + e -           Cl - D H = - 349 kJ/mol
                                E.A. = - 349 kJ/mol

Some other textbooks use a different sign
convention for the E.A. You need to be aware
of that when you are reading about this topic.
In those texts, the electron affinity for a chlorine
atom would be + 349 kJ/mol!

     F (g) + e -          F-     E.A. = - 328 kJ/mol

     O (g) + e -          O-     E.A. = - 141 kJ/mol

     O- +     e-          O 2- E.A. = + 880 kJ/mol

     O (g) + 2 e -          O 2- E.A. = + 739 kJ/mol
                                    DH = + 739 kJ/mol
So then why does oxygen usually have a -2 oxidation
state instead of a -1 oxidation state (Oxides are more
common than peroxides)???
    Na (g) + e -          Na -   E.A. = - 53 kJ/mol
                                 D H = - 53 kJ/mol
         Trends in Electron Affinities -
     Increases up a group.
     Increases from left to right in a period.


Li       Be      B     C      N      O      F

Na       Mg     Al     Si     P      S      Cl

K        Ca     Ga     Ge     As     Se     Br

Rb       Sr     In     Sn     Sb     Te      I

Cs       Ba     Tl     Pb     Bi     Po     At


To top