Absorption Spectra _amp; Quantum Mechanics

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Absorption Spectra _amp; Quantum Mechanics Powered By Docstoc
Spectra &
Light is both a wave and a
     Characteristics of Waves

• Wavelength
  – The distance between consecutive peaks or troughs

• Frequency
  – How many waves pass a point per second
• Speed
  – How fast a wave moves through space
    Electromagnetic Spectrum

• Forms of electromagnetic radiation
      gamma rays
      radio waves.
Electromagnetic Spectrum
Electromagnetic Spectrum
           • Visible light falls in the 400 to
             700 nm range
           • In the order of decreasing
              – Radio waves: 1 m
              – Microwave: 1 mm
              – Infrared radiation: 1 μm
              – Visible light: 500 nm
              – Ultraviolet radiation: 100 nm
              – X-rays: 1 nm
              – Gamma rays: 10-3 nm
          Atomic Spectra

• When visible light passes through a
  prism, its components separate into a
• White light, such as sun light or light
  from a regular light bulb, gives a
  continuous spectrum:
Wavelengths of Visible Light
Which Colour Has More
• If we look at light given off by electrified
  gases of elements and pass it through a
  prism then a unique and characteristic line
  spectra is seen for each.
                       Spectral Lines
• Bright spectrum lines can be seen when a chemical substance is
  heated and vaporized (Kirchhoff, ~1850)
• There are three different kinds of spectrum: continuous spectrum,
  emission-line spectrum, and absorption line spectrum
Emission-Line Spectra
              The Bohr Atom
• In 1913 Niels Bohr proposed that
  the energies of electrons inside
  atoms are quantized. By this he
  meant that the electrons could
  have only particular allowed

• This goes against the notions of
  classical physics as well as our
  own experiences.
• Niels Bohr, a student of Rutherford, studied
  the line spectra of the hydrogen atom to try
  to understand the electrons in the nuclear
  model of the atom.
• Bohr came up with a planetary model, in
  which electrons orbit the nucleus in circular
• His model was based on the idea that
  electrons and their energies are quantized:
  they can have only certain values.
                 The Bohr Atom

Small but discreet packets of
energy called quanta are
absorbed when an electron
jumps to a higher orbital and
emitted when an electron falls to
a lower orbital.
Electrons in an atom have their
energies restricted to certain
specific energy levels that
increase in energy as they
increase in distance from the
When you climb a stairs you
must be on a step to climb. You
can’t climb from between steps.
The higher you climb the greater
your potential energy relative to
Likewise electrons cannot be
between energy levels.
• In order to examine the
  difference between the
  energies      of     various
  energy levels the lowest-
  energy shell (n = 1) is set
  at 1.0 electron volt.
• We may determine the
  amount       of       energy
  between energy levels by
  subtracting the values
  from level to level.
• The diagram on the left indicates a hydrogen atom
  in the “ground state,” which is to say that the
  arrangement of electrons in the atom is of the
  lowest total energy.
• The diagram on the right indicates a hydrogen
  atom in an “excited state” - one of several
  possible excited states.
• The ground state of an atom is the condition
  when all the electrons of an atom occupy the
  lowest possible energy levels (those closest to
  the nucleus).
• If the atom absorbs energy, an electron can be
  raised to an excited state. The excited state is
  the condition at which at least one electron in an
  atom is at an energy level above the ground
• The atom must absorb the exact amount of
  energy required to raise the electron to the
  excited state. This may be done by heating the
  atom or by passing an electric current through a
• This explains why heated metals or gases glow
  a certain colour.
• An electron in an
  excited state is
  unstable. It falls back
  to the ground state,
  sometimes in one
  quantum jump,
  sometimes in two or
  more. In doing this, it
  releases a photon
  (packet) of light with a
  frequency proportional
  to the energy
  difference between
  the two levels.
     Bohr’s Atomic Model for Hydrogen
• The strongest hydrogen
  spectral line from the
  Sun, Hα line at 656 nm, is
  caused by electron-
  transition between n=3
  orbit and n=1orbit

• Lyman series lines:
  between n=1 orbit and
  higher orbits (n=2, n=3,

• Balmer series lines:
  between n-2 orbit and
  higher orbits (n=3, 4,
   Bohr’s theory depended on the
      following assumptions:
• An electron can travel indefinitely within an
  energy level without losing energy.
• The greater the distance between the nucleus
  and the energy level, the greater the energy
  required for an electron to travel in that energy
• An electron cannot exist between orbits, but can
  move to a higher unfilled orbit if it absorbs a
  specific amount of energy, and to a lower
  unfilled orbit if it loses energy.
• When an electron drops back to its original
  energy level, it is said to be in its ground state.
    Successes of the Bohr Model
•   Explained the stability of the atom.
•   Explained the atomic line spectrum of the
    hydrogen atom.
•   Introduced the concept of stationary
    energy levels.
•   Introduced the concept of quantized
•   Introduced a model of the atom that
    could be easily visualized.
       Failures of Bohr Model
• Did not explain the following:
  – Line spectra for many electron atoms
  – Electron configurations of many electron
  – The difference in energies of electrons
    occupying the same energy level.
  – The shapes and characteristics of molecules.
           spdf sublevels
• Bohr’s model of the hydrogen atom
  predicted the spectrum of hydrogen
  but failed for other elements because it
  required further sophistication. It was
  refined to include subshells.
• The principal energy levels are further
  divided into sublevels, labeled s, p, d,
  and f
• The number of sublevels equals the
  number of the principal energy level.
• Erwin Schrodinger
  created a model
  describing electrons
  as waves - known as
  wave mechanics
• won the Nobel Prize
  in Physics in 1933
• Although we cannot locate an electron
  precisely within an atom we can describe a
  region in space around the nucleus where
  there is a high probability of finding a given
• This region is called an orbital.
• n is the Principal Quantum Number. It is a
  positive whole number that specifies the
  energy level of an atomic orbital and its
  relative size. A higher n indicates an orbital
  with higher energy and larger size.
• The greatest number of electrons that are
  possible in any energy level is 2n2

n= 1   #electrons=2
n= 2   #electrons=8
n= 3   #electrons=18
n= 4   #electrons=32
Orbital Shape Quantum Number
• l= orbital shape quantum number. It
  indicates the shape of the sub-level.
• Has a maximum value of l=(n-1)
• So if n=1 l=0
•       n=2 l=1 or 0
•       n=3 l=2 or 1 or 0
•       n=4 l=3 or 2 or 1 or 0
•   When l=0   s-shape
•   When l=1   p-shape
•   When l=2   d-shape
•   When l=3   f=shape
           spdf sublevels
• The first principle energy level has one
  sublevel: (1s) (since n=1 has only 2e).
• The second level has two sublevels: (2s)
  and (2p) (since n=2 has only 8 e).
S orbital and p orbitals
P orbitals
            spdf sublevels
• The first principle energy level has one
  sublevel: (1s).
• The second level has two sublevels: (2s)
  and (2p).
• The third energy level has three sublevels:
  (3s), (3p) and (3d)
            spdf sublevels
• The first principle energy level has one
  sublevel: (1s).
• The second level has two sublevels: (2s)
  and (2p).
• The third energy level has three sublevels:
  (3s), (3p) and (3d)
• The fourth energy level has four sublevels:
  (4s), (4p), (4d), and (4f)
D orbitals
      The Magnetic Quantum #
• ml= The magnetic quantum number. It ranges in values
  from +l to –l with 0 included. It indicates the number of
• They may contain the following maximum electrons:
• s = 0 ml= 0  1 option so 1 s sub-level
• p = 1 ml= +1,0,-1  3 options so 3 p sub-levels
• d = 2 ml= +2,+1,0,-1,-2  5 options so 5 d sub-levels
• f = 3 ml= +3,+2,+1,0,-1,-2,-3  7 options so 7 f sub-

• Note that every sub-level has 2 electrons
               Filling Orbitals
1. No more than two electrons can occupy one
2. Electrons occupy the lowest energy orbitals
3. Each orbital on a sublevel is occupied by a
   single electron before a second electron
4. Oh what fun this is!!! I know you think so too.
   You are probably going to go home and tell
   your family all about this stuff tonight at dinner.
Permissible Quantum States
   Magnetic Spin Quantum Number
ms = spin magnetic  electron spin
       ms = ±½    (-½ = ) (+½ = )
Pauli exclusion principle states:
Each electron must have a unique set of 4 quantum numbers.
*What this means is that no more than two electrons
can occupy the same orbital, and that two electrons in
the same orbital must have opposite spins.

Electron spin is a purely quantum mechanical concept.
   How do we use these quantum
  numbers? We use them to write

Electron configurations of the first 11 elements, in subshell notation.
Notice how configurations can be built by adding one electron at a time.

                            Z    ground state electronic configuration
                     H      1    1s1
                     He     2    1s2
                     Li     3    1s2 2s1
                     Be     4    1s2 2s2
                     B      5    1s2 2s2 2p1
                     C      6    1s2 2s2 2p2
                     N      7    1s2 2s2 2p3
                     O      8    1s2 2s2 2p4
                     F      9    1s2 2s2 2p5
                     Ne     10   1s2 2s2 2p6
                     Na     11   1s2 2s2 2p6 3s1
Note: The energy levels do not go
in order. As a result you need the
Aufbau Principle to determine the
            Aufbau Principle
• States:
  – the number of electrons in
    an atom is equal to the
    atomic number;
  – each added electron will
    enter the orbitals in the
    order of increasing
  – an orbital cannot take
    more than 2 electrons.
            Orbital Box Diagrams
B                    2p
       1s       2s

C                    2p
                          Examples of ground state
       1s       2s
                          electron configurations in
N                    2p
                          the orbital box notation that
       1s       2s
                          shows electron spins  .

O                    2p
       1s       2s

F                    2p
       1s       2s

Cl                   2p
       1s       2s          3s          3p

Mn                   2p
       1s       2s          3s          3p

                     3d     4s
              Hund's Rule
• every orbital in a subshell is singly
  occupied with one electron before any one
  orbital is doubly occupied
• and all electrons in singly occupied orbitals
  must have the same spin.
            Orbital Box Diagrams
B                    2p
       1s       2s

C                    2p
       1s       2s
                          Look at the p subshells and
N                    2p
                          how the electrons are added
       1s       2s

O                    2p
       1s       2s

F                    2p
       1s       2s

Cl                   2p     3s
       1s       2s                    3p

Mn                   2p     3s
       1s       2s                    3p

            …               4s
• Now do the electron configurations and
  orbital box diagrams for the first 20
• Homework: page 136 #1-5, page 138 #1-
  2,5-6, page 145-146 #6
                Short Forms
• For atoms with many electrons, this notation can
  become lengthy.
• It is often abbreviated by noting that the first few
  subshells are identical to those of one or another
  noble gas.
• Phosphorus, for instance, differs from neon (1s2
  2s2 2p6) only by the presence of a third shell.
  Thus, the electron configuration of neon is pulled
  out, and phosphorus is written as follows:
  [Ne]3s2 3p3.
  Look at how the periodic table
takes electron configurations into
• Look at copper and chromium
• They do not follow the Aufbau principle
• Many of the transition elements like a half
  filled s sub-level.
• You need to know these exceptions
Element    Z   Electron configuration               Short electron conf.
                 2   2   6   2   6   2     1              2     1
Scandium   21 1s 2s 2p 3s 3p 4s 3d                  [Ar] 4s 3d
                 2   2   6   2   6   2     2              2     2
Titanium   22 1s 2s 2p 3s 3p 4s 3d                  [Ar] 4s 3d
                 2   2   6   2   6   2     3              2     3
Vanadium   23 1s 2s 2p 3s 3p 4s 3d                  [Ar] 4s 3d
                 2   2   6   2   6   1     5              1     5
Chromium   24 1s 2s 2p 3s 3p 4s 3d                  [Ar] 4s 3d
                 2   2   6   2   6   2     5              2     5
Manganese 25 1s 2s 2p 3s 3p 4s 3d                   [Ar] 4s 3d
                 2   2   6   2   6   2     6              2     6
Iron       26 1s 2s 2p 3s 3p 4s 3d                  [Ar] 4s 3d
                 2   2   6   2   6   2     7              2     7
Cobalt     27 1s 2s 2p 3s 3p 4s 3d                  [Ar] 4s 3d
                 2   2   6   2   6   2     8              2     8
Nickel     28 1s 2s 2p 3s 3p 4s 3d                  [Ar] 4s 3d
                 2   2   6   2   6   1     10             1     10
Copper     29 1s 2s 2p 3s 3p 4s 3d                  [Ar] 4s 3d
                 2   2   6   2   6   2     10             2     10
Zinc       30 1s 2s 2p 3s 3p 4s 3d                  [Ar] 4s 3d
                 2   2   6   2   6   10    2    1         10        2   1
Gallium    31 1s 2s 2p 3s 3p 3d           4s 4p     [Ar] 3d    4s 4p
Electron Configurations for Ions
• Because scandium is a metal in group 3
  on the periodic table it can lose three
  electrons and form +3 cation with the
  stable 3s23p6 configuration of argon.
•      Sc                    Sc3+ + 3e-

• [Ar] 3d1 4s2      [Ar] or [Ne] 3s2 3p6
Quantum "Addresses" for all the
      electrons in Neon
            1s2 2s2 2p6
      s (l=0)   p (l=1)   d (l=2)   f (l=3)







• Homework:
    • page 150 #10-13
    • page 165 #1-4
Variations in Ionization Energy
          What Happens?
• Draw the orbital box diagrams for Be and
  B, then N and O.
1s 22s2        2 2s2     1
             1s        2p

 Beryllium     Boron
1s2 2s2    2p3   1s2 2s2    2p4

Nitrogen           Oxygen
                 Chapter 4
• If you do not, you will suffer!!!!
• How can I make you suffer? Well on Friday you
  are going to be shown 5 substances and asked
  to figure out what kind of substances they are.
  There is NO LAB PROCEDURE!!! He
  heheehehe, you must design it yourself and then
  complete the lab on Monday March 26.

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