G' Rothstein

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Quantum Applets Relativistic Paradoxes

• G. Rothstein
• Physics/Pre-AP Physics
• Academics
• Townview Magnet Center

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• "If at first the idea is not absurd, then there
  is no hope for it. -Albert Einstein

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J. J. Thomson and The Atom

• Believed that a massive, positively charged
  substance filled the atom
• He pictured the electrons arranged within this
  substance like raisins in a muffin.

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Ernest Rutherford The Atom

• Rutherfords team bombarded metal (gold) foil
  with alpha particles. They measured the
  deflection of alpha particles directed normally
  onto a sheet of very thin gold foil. Under the
  prevailing plum pudding model, the alpha
  particles should all have been deflected by, at
  most, a few degrees. However they observed that a
  very small percentage of particles were deflected
  through angles much larger than 90 degrees.

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What are Alpha Particles?

• Alpha particles (named after the first letter in
  the Greek alphabet, a) consist of two protons and
  two neutrons bound together into a particle
  identical to a helium nucleus hence, it can be
  written as He2.
• Alpha particles are emitted by radioactive nuclei
  such as uranium or radium in a process known as
  alpha decay.

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What are Alpha Particles?

• Alpha particles consist of two protons and two
  neutrons that act as a single particle. An alpha
  particle is identical to the nucleus of a Helium
  atom. When alpha particles are emitted from an
  unstable radioactive nucleus, the atom is
  transmuted into a different element.

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Ernest Rutherford The Atom

• Top Expected results alpha particles passing
  through the plum pudding model of the atom
  undisturbed.Bottom Observed results a small
  portion of the particles were deflected,
  indicating a small, concentrated positive charge.
  

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• Observations
• Most of the alpha particles pass straight through
  the gold foil.
• Some of the alpha particles get deflected by very
  small amounts.
• A very few get deflected greatly.
• Even fewer get bounced of the foil and back to
  the left.
• Conclusions
• The atom is 99.99 empty space.
• The nucleus contains a positive charge and most
  of the mass of the atom.  
• The nucleus is approximately 100,000 times
  smaller than the atom.

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Ernest Rutherford Nuclear Model of the Atom

• Rutherford concluded that the results could be
  explained only if all the positive charge of the
  atom were concentrated in a tiny, massive central
  core. Rutherfords model is therefore called the
  nuclear model of the atom.

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A Planetary Model of the Atom

• The Bohr Model is probably familiar as the
  "planetary model" of the atom illustrated in the
  below figure that, for example, is used as a
  symbol for atomic energy.

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Atomic Spectra

• The set of light wavelengths emitted by an atom
  is called the atoms emission spectrum.
• The emission spectrum of an atom can be seen by
  looking at the light through a prism or a
  diffraction grating.

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Spectroscopy is the study of spectra, that is,
the dependence of physical quantities on
frequency.
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Atomic Spectra

• Emission spectrum of Hydrogen

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Emission Spectra of Hydrogen
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Atomic Spectra

• Emission spectrum of Iron - Each line corresponds
  to a particular wavelength of light emitted by
  the atoms of the gas.

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Max Planck - Quantum Theory

• Awarded the Nobel prize in 1918 for his discovery
  of the quantized nature of energy.
• The Energy of vibration of the atoms in a solid
  could only have specific frequencies as shown by
• E nhf where E Energy n is an integer such
  as 0,1,2,3 h 7 x 10-34 J/Hz f frequency

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Excitation by absorption of light and
de-excitation by emission of light
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Absorption Spectrum

• A gas that is cool and does not emit light will
  absorb light at characteristic wavelengths.

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Periodic Table Emission/Absorption Spectra Applets

• http//jersey.uoregon.edu/vlab/elements/Elements.h
  tml

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BOHRS ATOM APPLETS

• http//www.lon-capa.org/mmp/kap29/Bohr/app.htm
• http//physics.gac.edu/chuck/PRENHALL/Chapter203
  1/AABXTEI0.html

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Incandescent Bodies

• Incandescence is the release of thermal radiation
  from a body due to its temperature.
• Molten glassy material
• glows orange with
• incandescence.

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• The incandescent metal embers of the spark used
  to light this Bunsen burner emit light ranging in
  color from white to orange to red. This change
  correlates with their temperature as they cool in
  the air.

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• The temperature of lava flow can be estimated by
  observing its color. The color matches the
  measured temperatures of lava flows at about
  1,000 to 1,200 C.

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Radiation from Incandescent Bodies

• As the temperature increases, the frequency at
  which the maximum energy increases.

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The spectral class of stars is equivalent to a
classification of stars by their surface
temperature, with higher temperatures to the left.
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What is a Blackbody?

• An object is a "blackbody" if the radiation it
  emits into space originates completely from its
  temperature.

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Blackbody Radiation Applets

• http//www.mhhe.com/physsci/astronomy/applets/Blac
  kbody/frame.html
• http//www.lon-capa.org/mmp/applist/blackbody/bla
  ck.htm

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Instructions for Blackbody Radiation Experiment

• Using the applet (http//www.lon-capa.org/mmp/app
  list/blackbody/black.htm) find the
  wavelength(nm) and the temperature (K) for 25
  different temperatures. What happens to the peak
  as the temperature is increased in the applet.
  Use an excel spreadsheet for your data. Program
  the spreadsheet to find the frequency for each
  wavelength. Use the Chart Wizard in excel to
  plot Temperature vs. Wavelength. Describe the
  graph. Write an equation for the graph and
  discover the constant (if any).

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• A student recognizes Einstein in a train and
  asks Excuse me, professor, but does New York
  stop by this train?

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Relativity Review

• http//www.phys.unsw.edu.au/einsteinlight
• Twin paradox
• http//www.phys.unsw.edu.au/einsteinlight/jw/modul
  e4_twin_paradox.htm

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Relativistic Paradoxes

• This is a wheel, just an ordinary wheel, or is
  it?
• Each successive image in the movie is rotated by
  a small amount compared to the previous image.
• As the wheel rotates, the coordinates (x, y) of a
  point on the wheel relative to its centre change,
  but the distance r between the point and the
  centre remains constant
• r2 x2  y2 constant .

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Relativistic Paradoxes

• What would happen if the wheel moved at speeds
  close to the speed of light?
• We know that time slows down and lengths contract
  at relativistic speeds and mass increases. Or
  does it?

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Relativistic Paradoxes

• This is what a wheel looks like if the axle is
  moving at 87 of the speed of light. The
  cartwheel appears Lorentz contracted along the
  direction of motion.
• The bottom of the cartwheel, where it touches the
  road, is not moving, and is not Lorentz
  contracted. You might think that the top of the
  cartwheel would have to move faster than the
  speed of light to overtake the axle moving at 87
  of the speed of light but of course it can't.

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• The cartwheel offers another example of the
  impossibility of completely rigid bodies in
  special relativity. In the frame of reference of
  someone riding on the axle (but not rotating),
  the rim is whizzing around and is Lorentz
  contracted, while the spokes that are moving
  transversely are not contracted. Something must
  give the rim must stretch, or the spokes
  compress.

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• A Black Hole is a tunnel at the end of light.

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Relativistic Pizza Paradox

• What would happen if the pizza moved at speeds
  close to the speed of light? Would someone be
  able to eat it? Would there be more pizza or
  less pizza?
• We know that time slows down and lengths contract
  at relativistic speeds and mass increases. Or
  does it?

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Solution

• Does this mean you go faster than the speed of
  light? No. From the point of view of a person at
  rest on Earth, you never go faster than the speed
  of light. From your own point of view, distances
  along your direction of motion are
  Lorentz-contracted, so distances that are vast
  from Earth's point of view appear much shorter to
  you. Fast as the Universe rushes by, it never
  goes faster than the speed of light.

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Solution

• It would take a huge amount of energy to keep you
  accelerating at g. Also, you would use up a huge
  amount of Earth time traveling around at
  relativistic speeds. If you took a trip to the
  edge of the Universe, then by the time you got
  back not only would all your friends and
  relations be dead, but the Earth would probably
  be gone, swallowed by the Sun in its red giant
  phase, the Sun would have exhausted its fuel and
  shriveled into a cold white dwarf star, and the
  Solar System, having orbited the Galaxy a
  thousand times, would be lost somewhere in its
  milky ways.

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credits

• http//casa.colorado.edu/ajsh/sr/contraction.html
  
• http//en.wikipedia.org/wiki/Special_relativity
• http//www.phys.unsw.edu.au/einsteinlight/
• http//www.thinkarete.com/quotes/by_teacher/albert
  _einstein/