special relativity…continued, diffraction grating equation and photo-electric effect relativistic...
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Special Relativity…continued, Diffraction Grating Equation and Photo-electric effect
•Relativistic Doppler Shift•Relativistic Momentum and Energy•Diffraction Grating Equation•Photo-electric effect•Homework Hints…
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Relativistic Doppler Shift• Doppler Shift for Sound,
vs=speed of sound
vr=radial velocity of source
• Relativistic Doppler Shift– Time Dilation
– Varying distance
For =0 or 180, then:
Transverse Doppler Shift =90
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Relativistic Doppler ShiftRedshift/Blueshift parameter z
(radial motion)
(radial motion)
Measure redshift Measure recession velocity!!!
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Relativistic Doppler ShiftRedshift/Blueshift
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Relativistic Velocity Transformations
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Relativistic Headlight Effectexample 4.3.3
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Relativistic Momentum and Energy
Kinetic Energy
Total Energy
Rest Energy
Momentum Energy Relation
Momentum
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Relativistic Momentum and EnergyThe Derivation of E=mc2
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Relativistic Momentum and EnergyThe Derivation of E=mc2
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Relativistic Momentum and Energy
Derivation pages 105-106
Newtonian Mechanics “breaks down” at high speed v-->c.
does not hold.
However
does still hold if the momentum becomes….
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Four-Vectors
Space-time four-vector
Invariant length
Energy-Momentum four-vector
Invariant length
Lorentz Transformation Lorentz Transformation
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Spectral LinesApplication of Spectral Measurements
• Stellar Doppler Shift• Galactic Doppler Shifts• Quasar Doppler Shifts
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Radial Velocities
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Spectral LinesSpectrographs
• Spectroscopy• Diffraction grating equation
(n=0,1,2,…)
n = order
• Resolving Power
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Photoelectric Effect
Classical Expectations•Kinetic energy of ejected electrons should depend on strength of electric field and therefore intensity of light and not the number of ejected electrons.
•Maximum kinetic energy of ejected electrons should not depend on frequency of light.
•Any frequency light should be capable of ejecting electrons.
Observations•Kinetic energy of ejected electrons does not depend on intensity of light!
•Increasing intensity will produce more ejected electrons.
•Maximum kinetic energy of ejected electrons depends on frequency of light.
•Frequency must exceed cutoff frequency before any electrons are ejected
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Photoelectric Effect
Einstein took Planck’s assumption of quantized energy of EM waves seriously. Light consisted of massless photons whose energy was:
Einstein was awarded the Nobel Prize in 1921 for his work on the photo-electric effect
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Photo-electric Effect
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Inertial reference frameRemember that the clocks are located at every point in space
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Example 4.3.2 useful
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Time Dilation…Light Clock
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Worked Problems
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Worked Problem
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