Transcript Monday, February 8, 2010

Physics 3313 - Lecture 6
Monday February 8, 2010
Dr. Andrew Brandt
1.
2.
3.
4.
5.
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HW1 Due today HW2 weds 2/10
Electron+X-rays
Black body radiation
Compton Effect
Pair Production
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CHAPTER 3
The Experimental Basis of Quantum Theory
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•
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•
•
•
•
•
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3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
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Discovery of the X Ray and the Electron
Determination of Electron Charge
Line Spectra (defer to next chapter)
Quantization
Blackbody Radiation
Photoelectric Effect (last lecture)
X-Ray Production
Compton Effect
Pair Production and Annihilation
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1895 J.J. Thomson’s Discover’s Electron
• Thomson used an evacuated cathode-ray tube (vacuum tube with a high
voltage) to show that the cathode rays were negatively charged particles
(electrons) by deflecting them in electric and magnetic fields.

Used force equations to determine q/m for electron, charge later
determined by Millikan Oil drop experiment
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Thomson’s Experiment
• Thomson’s method of measuring the ratio of the electron’s
charge to mass was to send electrons through a region
containing a magnetic field perpendicular to an electric field.
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Calculation of e/m

An electron moving through the electric field is
accelerated by a force:

Electron angle of deflection:

The magnetic field deflects the electron against the
electric field force.

The magnetic field is adjusted until the net force is zero.

Charge to mass ratio:
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Calculation of the oil drop charge
• Used an electric field and
gravity to suspend a
charged oil drop.
• Mass is determined from
Stokes’s relationship of the
terminal velocity to the
radius and density.
• Magnitude of the charge on
the oil drop.
• Thousands of experiments
showed that there is a basic
quantized electron charge.
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C
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3.5: Blackbody Radiation
• When matter is heated, it emits radiation (visible light, CW
blacksmith, Return of King).
• All objects radiate energy continuously with a frequency that
depends on temperature.
• Ability to radiate related to ability to absorb—thermal
equilibrium
• Black body is ideal object that absorbs all radiation
independent of frequency (radiation enters small whole
bounces around until absorbed)
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Rayleigh-Jeans Formula
• Lord Rayleigh used the classical theories of electromagnetism
and thermodynamics to show that the blackbody spectral
distribution should be
• Missed it by that much! The disagreement for small
wavelengths (data goes to zero while theory increases with 4th
power!) became known as “the ultraviolet catastrophe” and
was one of the outstanding exceptions that classical physics
could not explain.
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Planck’s Radiation Law
•
Planck assumed that the radiation in the cavity was
emitted (and absorbed) by some sort of “oscillators” that
were contained in the walls. He used Boltzman’s statistical
methods to arrive at the following formula that fit the
blackbody radiation data (note exponential damping at
small wavelengths!)
Planck’s radiation law
•
Planck made two modifications to the classical theory:
1)
2)
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The oscillators (of electromagnetic origin) can only have certain
discrete energies determined by En = nhf, where n is an integer, f is
the frequency, and h is called Planck’s constant.
h = 6.6261 × 10−34 J·s.
The oscillators can absorb or emit energy in discrete multiples of the
fundamental quantum of energy given by
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Wien’s Displacement Law
• The intensity (λ, T) is the total power radiated per unit area
per unit wavelength at a given temperature.
• Wien’s displacement law: The maximum of the distribution
(from taking derivative with respect to wavelength) shifts to
smaller wavelengths as the temperature is increased.
• Ex: 2.7K cosmic background
radiation from Big Bang 1.1 mm
microwaves in 1964 sky survey
(1978 Nobel prize for Penzias+Wilson)
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Stefan-Boltzmann Law
• Can also use Planck’s formula to derive an expression for the
total power radiated increases with the temperature:
• This is known as the Stefan-Boltzmann law, with the constant
σ experimentally measured to be 5.6705 × 10−8 W / (m2 · K4).
• The emissivity є (є = 1 for an idealized blackbody) is simply the
ratio of the emissive power of an object to that of an ideal
blackbody and is always less than 1.
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What is Light?
• Both wave and particle theory needed.
• Quantum theory: light has individual photons… but frequency is a wave
phenomenon
• Two different interpretations of intensity
2
• Wave theory I   0 cE average magnitude of EM wave over a complete
cycle
• Photon description I=Nh
2
• Both descriptions must give the same intensity if they are valid so N  E
• Consider double slit experiment: for large N observer looking at screen
would see a double slit interference pattern (continuous distribution)
• However, for small N, see a flash of light as one photon at a time goes
through either slit (quantum phenomena), but if you wait a long time you
would see an interference pattern
• How can photon interfere with itself ? (sounds vaguely immoral)
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What is Light (2)?
2
• Must conclude that E is the probability of finding a photon at a certain
place and time—each photon has a wave associated with it; the intensity of
wave a given place on the screen determines the likelihood that a photon
will arrive there
• Light travels as a wave, but deposits and absorbs energy like a particle (or a
series of particles)
• Wave-particle duality: need both pictures (outside of our everyday life
experience!)
• It not a wave nor a particle…it’s a WARTICLE
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X-Rays
• 1895 Roentgen found that when fast moving electrons strike matter a
highly penetrating unknown radiation (X-Ray) is produced. He found
certain characteristics of X-Rays: they
1) travel in straight lines
2) are unaffected by E+B fields (what does this imply?)
3) can pass through opaque materials
4) can expose photographic plates
• He also observed that faster electrons yield more penetrating X-Rays
and that increasing the number of incident electrons yields higher intensity
X-Rays
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More X-Rays
• Soon it became obvious that X-Rays are EM waves
• Accelerating charges produce EM waves (basis for radio
transmitters)
• How does an electron produce X-Rays?
• What happens as an electron interacts with matter?
• It decelerates: bremsstrahlung (“braking radiation”)
• Higher atomic number nuclei cause more energetic brem.
(energy loss is more important for light particles like
electron—NLC)
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Measuring X-Ray Wavelength
•
•
•
Scattering of X-Rays off Crystal (draw)
Use crystals as a diffraction gratingneed crystals since d must be on order of a
wavelength () for diffraction effects to be observed and  is very small (0.01
to 10 nm) for X-Rays.
Small wavelength implies large , so if X-Ray has several orders of magnitude
smaller wavelength than light, it has several orders of magnitude higher energy
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http://www.wwnorton.com/college/chemistry/gilbert/tutorials/ch10.htm
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Inverse P.E. Effect
• X-Ray production is an inverse photoelectric effect: electron in/photon out,
instead of vice-versa
• Small wavelength implies large , so if X-Ray has several orders of
magnitude smaller wavelength than light, it has several orders of magnitude
higher energy
• For photoelectric effect: KEmax  eV0  h  
• For X-Rays can neglect binding energy, since X-Ray is so energetic: eV  hvmax
where V is the accelerating potential of X-Ray machine and the frequency
is maximum when the electron gives all of its energy to a single photon
• Duane-Hunt formula for X-Ray production:
min
hc 1.24 106


V m
eV
V
http://www.spineuniverse.com/videos/x-rays/
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Compton Effect
• Can photon be treated like a particle when it interacts with an electron?
• Consider conservation of momentum and energy, and also have an
additional constraint that the loss in photon energy yields an equivalent
gain in electron KE: hv  hv  KE
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Compton Effect
• some math occurs on blackboard yielding:
h
•
where c 
is called the Compton
mc
Wavelength, and has a value of 2.4 pm for electrons
• this is largest when?
h
   
(1  cos  )
mc
 
• Compton scattering is the main way that X-Rays lose energy when passing
through matter; visible light has long wavelength so small wavelength shift
is less noticeable
• Experimentally Compton effect initially not verified!
• The problem was that electrons in matter are not free—some are tightly
bound and if whole atom recoils the large mass implies a small wavelength
shift (when this is corrected for, the Compton picture is validated)
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Other X-ray stuff
• http://www.nature.com/news/2009/090728/full/news.2009.744.html
• http://www.livescience.com/strangenews/reason_demkina_050128.html
• http://www.dailymotion.com/video/x1z82o_xray-vision_creation
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Pair Production
• In pair production a photon of sufficient energy can create an
electron/positron pair.
• How much energy?
•  2me c 2  .511MeV  2
• Charge conserved, for energy and momentum conservation need the
nucleus (Ex. 2.5)
• Opposite of pair production is annihilation e  e   
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Energy Loss in Matter
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Photons and Gravity
E  pc  h
h
p
c
h
mv 
c
hv
m 2
c
for v=c
effective mass of photon, implies light affected by gravity
Black hole—so much gravitational force that photons cannot escape
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