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					    A Day in the Life of a Nanoparticle

     Or how I learned to not sunburn and still look good.




                                                http://media.photobucket.com/imag
                                                e/sunscreen%20and%20nanopartic
                                                les/vivawoman/badger-spf30-
                                                sunscreen.jpg

http://www.wsu.edu/~jtd/physunder/physun2.jpg                                       http://www.rdecom.army.mil/rdemagazine/20040
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             Nanoparticle Uses
   Sunscreens
   Make-up
   Automotive Paint
   Sporting Goods
   anti-bacterial
                       Hong Dong


                       FE-SEM: Zeiss(1550)-Clark


                       This image shows electrospun nylon 6 nanofibers decorated with surface bound Ag nanoparticles.
                       Immersing nylon 6 nanofibers into Ag colloidal solution with pH 5, Ag nanoparticles were assembled
                       onto nylon 6 nanofibers via interaction between nylon 6 and protection groups of Ag nanoparticles.
                       Future applications include antibacterial filtration.


                       Fiber Science and Apparel Design


                       Advisor     Juan Hinestroza
☻   When physicists first began investigating the structure of
    atoms in the early 1900s, they uncovered a strange new
    world. The subatomic particles they found -- electrons,
    protons, and neutrons -- seemed to behave according to
    a completely different set of laws than those governing
    our everyday world.


☻ Then, in the late 1920s, a team of young physicists led
  by Niels Bohr introduced a theory that explained the
  behavior of atoms and their particles. Not surprisingly,
  the theory, called quantum mechanics, was as bizarre
  as the world it attempted to explain.
☻ Rather than identifying precisely where an electron should
  be, for example, quantum mechanics predicts only the
  probability of finding that electron in one place or another.


☻ This description of unpredictability at the atomic level --
  indeed, at any level -- was completely unacceptable to
  Einstein; it flew in the face of everything he believed, and
  directly contradicted his orderly theories of the universe.


☻ Despite Einstein's disapproval, quantum mechanics has only
  grown in acceptance as a theory.
           The Quantum Café –
           Michael Greene




http://www.pbs.org/wgbh/nova/programs/ht/qt/3012_qd_05.html
Opinions on quantum mechanics
                                  I think it is safe to say that no
                                  one understands quantum
                                  mechanics. Do not keep saying
                                  to yourself, if you can possibly
                                  avoid it, “But how can it be like
                                  that?” because you will get
                                  “down the drain” into a blind
                                  alley from which nobody has yet
                                  escaped. Nobody knows how it
                                  can be like that.

                                               - Richard Feynman


                                  Those who are not shocked
                                  when they first come across
                                  quantum mechanics cannot
                                  possibly have understood it.
   Richard Feynman (1918-1988)‫‏‬                        - Niels Bohr
 Important Questions
# How did our understanding of the atom
  change in the 1920s?

# How did quantum mechanics contradict
  Einstein's view of physics? What did Einstein
  mean when he said, "God does not throw
  dice"?

# What are some of the "bizarre" things that
  quantum mechanics predicts?
The Birth of Modern Physics


Classical Physics of the 1890s
The Kinetic Theory of Gases
Waves and Particles
Conservation Laws and Fundamental Forces
The Atomic Theory of Matter
Outstanding Problems of 1895 and New
   Horizons
                                                           James Clerk Maxwell

  The more important fundamental laws and facts of physical science have all
  been discovered, and these are now so firmly established that the possibility
  of their ever being supplanted in consequence of new discoveries is
  exceedingly remote… Our future discoveries must be looked for in the sixth
  place of decimals. - Albert A. Michelson, 1894


  There is nothing new to be discovered in physics now. All that remains is more
  and more precise measurement. - Lord Kelvin, 1900
Classical Physics of the 1890s


  Mechanics →




                Electromagnetism‫→‏‬




                              ←‫‏‬Thermodynamics
Electromagnetism culminated
with Maxwell’s Equations


 Gauss’s‫‏‬law:
    (electric field)‫‏‬
                         E  q / 0

 Gauss’s‫‏‬law:                           James Clerk Maxwell
    (magnetic field)‫‏‬     B  0          (1831-1879)‫‏‬


 Faraday’s‫‏‬law:
                         
                        E 
                            B
                            t            in the presence of
                                          only stationary
 Ampère’s law:                            charges.
                              E
                            
                        B  0
                          0
                               t
Faraday saw the World in a new way!
The Nature of Light

 Newton promoted the corpuscular
   (particle) theory

   Particles of light travel in straight lines
     or rays
   Explained sharp shadows
   Explained reflection and refraction



                                                          Newton in action



                               "I procured me a triangular glass prism to try
                               therewith the celebrated phenomena of
                               colours." (Newton, 1665)
The Nature of Light

Huygens promoted the wave theory.

    He realized that light propagates as a
    wave from the point of origin.
    He realized that light slowed down on
    entering dense media.                           Christiaan Huygens
                                                       (1629-1695)‫‏‬


                                    He explained polarization,
                                    reflection, refraction, and double
                                    refraction.

           Double refraction
 Diffraction confirmed light to be a wave.

   While‫‏‬scientists‫‏‬of‫‏‬Newton’s‫‏‬time‫‏‬thought‫‏‬
   shadows‫‏‬were‫‏‬sharp,‫‏‬Young’s‫‏‬two-slit
   experiment could only be explained by
   light behaving as a wave. Fresnel
   developed an accurate theory of diffraction
   in the early 19th century.


                 Diffraction patterns


 One slit
                                                 Augustin Fresnel
Two slits
Waves can interfere.
Maxwell strove to prove his Mentor correct
Light waves were found to be solutions to
Maxwell’s Equations.

The electromagnetic spectrum is vast.




                                        visible
  microwave             infrared                  UV            X-ray




         106      105
 radio                                                                gamma-ray
                             wavelength (nm)‫‏‬

     All electromagnetic waves
        travel in a vacuum with
        a speed c given by:


where μ0 and ε0 are the permeability and permittivity of free space
Light is an electromagnetic wave.

The electric (E) and magnetic (B) fields are in phase.




The electric field, the magnetic field, and the propagation direction are
all perpendicular.
Triumph of Classical Physics:
The Conservation Laws
Conservation of energy: The sum of energy
  (in all its forms) is conserved (does not
  change) in all interactions.

Conservation of linear momentum: In the
  absence of external forces, linear
  momentum is conserved in all interactions.

Conservation of angular momentum: In the
  absence of external torque, angular
  momentum is conserved in all interactions.

Conservation of charge: Electric charge is     These laws remain
                                               the key to interpreting
  conserved in all interactions.               even particle physics
                                               experiments today.
Problems in 19th-century physics

In a speech to the Royal Institution in 1900, Lord Kelvin himself
   described‫‏‬two‫“‏‬dark‫‏‬clouds‫‏‬on‫‏‬the‫‏‬horizon”‫‏‬of‫‏‬physics:



 The question of the existence
 of an electro-magnetic
 medium—referred to as
 “ether”‫‏‬or‫“‏‬aether.”‫‏‬

 The failure of classical
 physics to explain blackbody
 radiation.
The Ultraviolet Catastrophe
Lord Rayleigh used the classical theories of electromagnetism
  and thermodynamics to show that the blackbody spectrum
  should be:



Rayleigh-Jeans Formula




This worked at longer wavelengths but deviates badly at short ones.
This problem became known as the ultraviolet catastrophe and was one of
the‫‏‬many‫‏‬effects‫‏‬classical‫‏‬physics‫‏‬couldn’t‫‏‬explain.
More problems: discrete spectral lines

For reasons then unknown, atomic gases emitted only certain narrow
frequencies, unique to each atomic species.




                                                                     Emissio
                                                                     n
                                                                     spectra
                                                                     from
                                                                     gases of
                                                                     hot
                                                                     atoms.

                        Wavelength
Additional discoveries in 1895-7 contributed to the
complications.


  X-rays (Roentgen)‫‏‬

  Radioactivity (Becquerel)‫‏‬

  Electron (Thomson)‫‏‬

  Zeeman effect




                    Roentgen’s‫‏‬x-ray
                    image‫‏‬of‫‏‬his‫‏‬wife’s‫‏‬hand‫‏‬
                    (with her wedding ring)‫‏‬
The Beginnings of Modern Physics

These new discoveries and the
  many resulting complications
  required a massive revision of       c
  fundamental physical




                                             Quantum mechanics




                                                                              General relativity
  assumptions.
                                                                  Special
                                                                 relativity
The introduction (~1900) of the




                                     Speed
  modern theories of special
  relativity and quantum
  mechanics became the
  starting point of this most                                       19th-
  fascinating revision. General                                   century
  relativity (~1915) continued it.     0                          physics
                                                                 Log
                                                                 (size)‫‏‬
Triumph of Classical Physics:
The Conservation Laws
Conservation of energy: The sum of energy
  (in all its forms) is conserved (does not
  change) in all interactions.

Conservation of linear momentum: In the
  absence of external forces, linear
  momentum is conserved in all interactions.

Conservation of angular momentum: In the
  absence of external torque, angular
  momentum is conserved in all interactions.
                                               These laws remain
Conservation of charge: Electric charge is     the key to interpreting
                                               even particle physics
  conserved in all interactions.               experiments today.
For our sunscreen to work we will need to look
at an experiment designed to determine how
tightly bound electrons are to a surface.


   This requires coming up with Planck's Constant.

   This also requires the determination of the work Function.
   Work function experiment.



Workfunction for ZnO is ~4.5




         http://www.walter-fendt.de/ph11e/photoeffect.htm
          What is Quantum Physics?
   Quantum physics is a branch of Science
    that deals with discrete, indivisible units of
    energy called quanta as described by
    Quantum Theory.
   There are five main ideas represented in
    Quantum Theory which are:
    1. Energy is not continuous, but comes in
    small, but discrete units.
    2. The elementary particles behave both
    like particles and like waves.
    3. The movement of these particles is
    inherently random.
    4. It is physically impossible to know both
    the position and momentum of a particle at
    any instant in time so that the more accurate
    the measurement of one is, the more
    inaccurate the measure of the other is.
    5. The atomic world is NOTHING like the
    world we live in.
Structure of the Atom


The Atomic Models of Thomson and
   Rutherford
Rutherford Scattering
The Classic Atomic Model
The Bohr Model of the Hydrogen Atom
Successes & Failures of the Bohr Model
Characteristic X-Ray Spectra and Atomic                       Niels Bohr (1885-1962)
   Number
Atomic Excitation by Electrons
 The opposite of a correct statement is a false statement. But the opposite of a
 profound truth may well be another profound truth.
 An expert is a person who has made all the mistakes that can be made in a very
 narrow field.
 Never express yourself more clearly than you are able to think.
 Prediction is very difficult, especially about the future.
                                                                      - Niels Bohr
Structure of the Atom

Evidence in 1900 indicated that
the atom was not a fundamental unit:

    1)   There seemed to be too many kinds
         of atoms, each belonging to a distinct chemical
         element (way more than earth, air, water, and fire!).
    2)   Atoms and electromagnetic phenomena were intimately
         related (magnetic materials; insulators vs. conductors;
         different emission spectra).
    3)   Elements combine with some elements but not with others,
         a characteristic that hinted at an internal atomic structure
         (valence).
    4)   The discoveries of radioactivity, x rays, and the electron (all
         seemed to involve atoms breaking apart in some way).
Knowledge of atoms in 1900


Electrons (discovered in
1897) carried the negative
charge.
Electrons were very light,
even compared to the atom.
Protons had not yet been
discovered, but clearly
positive charge had to be
present to achieve charge
neutrality.
Thomson’s
Atomic Model

Thomson’s‫“‏‬plum-pudding”‫‏‬
model of the atom had the
positive charges spread
uniformly throughout a
sphere the size of the atom,
with electrons embedded in
the uniform background.


In‫‏‬Thomson’s‫‏‬view,‫‏‬when‫‏‬the‫‏‬atom‫‏‬was‫‏‬heated,‫‏‬the‫‏‬electrons‫‏‬could‫‏‬
vibrate about their equilibrium positions, thus producing
electromagnetic radiation.
Unfortunately,‫‏‬Thomson‫‏‬couldn’t‫‏‬explain‫‏‬spectra‫‏‬with‫‏‬this‫‏‬model.
Experiments of Rutherford, Geiger and
Marsden
 Rutherford, Geiger, and Marsden
 conceived a new technique for
 investigating the structure of
 matter by scattering a particles
 from atoms.
Experiments of Rutherford, Geiger and
Marsden 2
 Geiger showed that many a particles were scattered from thin
 gold-leaf targets at backward angles greater than 90°.
Rutherford’s Atomic Model


 Experimental results       Ernest Rutherford
                              (1871-1937)
 were not consistent with
 Thomson’s‫‏‬atomic‫‏‬model.

 Rutherford proposed that
 an atom has a positively
 charged core (nucleus)
 surrounded by the
 negative electrons.

 Geiger and Marsden
 confirmed the idea in
 1913.
The Classical Atomic Model

Consider an atom as a planetary system.
The‫‏‬Newton’s‫2‏‬nd Law force of attraction on
the electron by the nucleus is:
                 1 e2 mv2
           Fe            
                4 0 r 2
                            r
where v is the tangential velocity of the
electron:
                 e                              e2
      v                     K  1 mv2  1
             4 0 mr             2       2
                                              4 0 r
The total energy is then:
                                                     This is negative, so
                                                     the system is bound,
                                                     which is good.
The Planetary Model is Doomed
From classical E&M theory, an accelerated electric charge radiates
energy (electromagnetic radiation), which means the total energy
must decrease. So the radius r must decrease!!




                                           Electron
                                           crashes
                                           into the
                                          nucleus!?




Physics‫‏‬had‫‏‬reached‫‏‬a‫‏‬turning‫‏‬point‫‏‬in‫‏0091‏‬with‫‏‬Planck’s‫‏‬
hypothesis of the quantum behavior of radiation, so a radical
solution would be considered possible.
The Bohr Model of the Hydrogen Atom

Bohr’s‫‏‬general‫‏‬assumptions:                               n=1
                                            n=2
1. Stationary states, in which orbiting
electrons do not radiate energy, exist in
atoms and have well-defined energies,
En. Transitions can occur between them,
yielding light of energy:
          E = En −‫‏‬En’ = h

2. Classical laws of physics do not apply
to transitions between stationary states,                n=3
but they do apply elsewhere.


                                                    Angular
 3. The angular momentum of the nth state is: n 
                                                    momentum is
 where n is called the Principal Quantum Number.    quantized!
Consequences of the Bohr Model

The angular momentum is:

            L  mvr  n

So the velocity is:      v  n / mr
                    e                  n2 2     e2          a0
But:   v                       So:         
                  4 0 mr              2 2
                                       mr     4 0 mr

                                                         4 0   2
Solving for rn:         rn  n 2 a0        where:   a0 
                                                          me 2

a0 is called the Bohr radius. It’s the diameter of the Hydrogen
atom (in its lowest-energy, or “ground,” state).
Bohr Radius
The Bohr radius,

                    4 0   2
               a0 
                     me 2

is the radius of the unexcited hydrogen atom and is equal to:


                                     /


The‫“‏‬ground”‫‏‬state‫‏‬Hydrogen‫‏‬atom‫‏‬diameter‫‏‬is:
The Hydrogen
Atom Energies
Use the classical
result for the             e2
                  E   
energy:                  8 0 r
             4 0 n 2   2

and:    rn 
               me 2
So the energies of the stationary
states are:




or:     En =  E0/n2

              where E0 = 13.6 eV.
The Hydrogen Atom
Emission of light occurs when the atom is in an excited state
and decays to a lower energy state (nu →‫‏‬nℓ).

                         h  Eu  E

where  is the frequency of a photon.

              1   h
                    
               c hc

R∞ is the Rydberg constant.

                               me4
                       R 
                            (4 )3 c 0 2
Transitions
in the
Hydrogen
Atom

 The atom will remain
    in the excited state
         for a short time
      before emitting a
 photon and returning
  to a lower stationary
  state. In equilibrium,
   all hydrogen atoms
           exist in n = 1.
Characteristic X-Ray
Spectra and Atomic
Number
Shells have letter names:
        K shell for n = 1
        L shell for n = 2



The atom is most stable in its
ground state.
An electron from higher
shells will fill the inner-shell vacancy at lower energy.

When it occurs in a heavy atom, the radiation emitted is an x-ray.
It has the energy E (x-ray) = Eu −‫‏‬Eℓ.
The Correspondence
Principle


Bohr’s‫‏‬correspondence‫‏‬principle‫‏‬
is rather obvious:



         In the limits where classical and
         quantum theories should agree,
         the quantum theory must reduce
         the classical result.
Successes and Failures of the Bohr
Model
Success:
The electron and
hydrogen nucleus
actually revolve
about their mutual
center of mass.
The electron mass is replaced
by its reduced mass:



The Rydberg constant for infinite nuclear mass, R∞, is replaced by R.
Limitations of the
Bohr Model
The Bohr model was a great
step in the new quantum
theory, but it had its limitations.


Failures:
    Works only for single-electron‫“(‏‬hydrogenic”)‫‏‬atoms.

    Could not account for the intensities or the fine structure of
    the spectral lines (for example, in magnetic fields).

    Could not explain the binding of atoms into molecules.

				
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