Quantum Applets &
Relativistic Paradoxes
G. Rothstein
Physics/Pre-AP Physics
Academics
Townview Magnet Center
• "If at first the idea is not absurd, then there
is no hope for it.”
-Albert Einstein
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.
Ernest Rutherford & The Atom
• Rutherford’s 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.
What are Alpha Particles?
• Alpha particles (named after the first letter in the
Greek alphabet, α) 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.
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.
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.
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. Rutherford’s model is therefore called the
nuclear model of the atom.
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.
Atomic Spectra
• The set of light wavelengths emitted by an
atom is called the atom’s emission
spectrum.
• The emission spectrum of an atom can be
seen by looking at the light through a
prism or a diffraction grating.
Spectroscopy is the study of
spectra, that is, the dependence of
physical quantities on frequency.
Atomic Spectra
• Emission spectrum of Hydrogen
Emission Spectra of Hydrogen
Atomic Spectra
• Emission spectrum of Iron - Each line
corresponds to a particular wavelength of light
emitted by the atoms of the gas.
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 1034 J/Hz; f = frequency
Excitation by absorption of light
and de-excitation by emission of
light
Absorption Spectrum
• A gas that is cool and does not
emit light will absorb light at
characteristic wavelengths.
Periodic Table
Emission/Absorption Spectra
Applets
• http://jersey.uoregon.edu/vlab/elements/El
ements.html
BOHR’S ATOM APPLETS
• http://www.loncapa.org/~mmp/kap29/Bohr/app.htm
• http://physics.gac.edu/~chuck/PRENHALL
/Chapter%2031/AABXTEI0.html
Incandescent Bodies
• Incandescence is the release of thermal
radiation from a body due to its
temperature.
• Molten glassy material
glows orange with
incandescence.
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.
• 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.
Radiation from Incandescent
Bodies
• As the temperature increases, the
frequency at which the maximum energy
increases.
The spectral class of stars is equivalent to a
classification of stars by their surface temperature,
with higher temperatures to the left.
What is a Blackbody?
• An object is a "blackbody" if the radiation it
emits into space originates completely
from its temperature.
Blackbody Radiation Applets
• http://www.mhhe.com/physsci/astronomy/a
pplets/Blackbody/frame.html
• http://www.loncapa.org/~mmp/applist/blackbody/black.ht
m
Instructions for Blackbody
Radiation Experiment
• Using the applet (http://www.lon-
capa.org/~mmp/applist/blackbody/black.ht
m) 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).
• A student recognizes Einstein in a train
and asks: Excuse me, professor, but does
New York stop by this train?
Relativity Review
• http://www.phys.unsw.edu.au/einsteinlight
• Twin paradox
• http://www.phys.unsw.edu.au/einsteinlight/j
w/module4_twin_paradox.htm
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 .
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?
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.
• 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.
• A Black Hole is a tunnel at the end of light.
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?
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.
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.
credits
• http://casa.colorado.edu/~ajsh/sr/contracti
on.html
• http://en.wikipedia.org/wiki/Special_relativit
y
• http://www.phys.unsw.edu.au/einsteinlight/
• http://www.thinkarete.com/quotes/by_teac
her/albert_einstein/