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R. J. Wilkes
Email: [email protected]
Physics 116
Session 30 Blackbody radiation and the photoelectric effect
Nov 18, 2011
Announcements:
â˘! Updated quiz score totals will be posted on WebAssign tomorrow
â˘! Nice series on PBS covering topics we will discuss in class:
Brian Greeneâs Fabric of the Cosmos
http://www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.html
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Lecture Schedule (up to exam 3)
Today
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General relativity
â˘! Einstein, 1915: extended relativity to accelerated frames: general relativity
â! GR really describes the geometry of spacetime: gravity of massive objects warps spacetime in their vicinity
â! Equivalence Principle: Observations cannot distinguish a uniformly accelerated frame from a uniform gravity field
â! Eddington, 1919: GR predictions matched observed anomalies in orbit of Mercury, Newtonian predictions do not â Einstein is right*
â˘! More predictions and consequences of GR:
â! Gravitational time dilation and redshift
â! Deflection of light by gravity
â! Gravitational waves
â! Black holes
â˘! Applications confirming GR today
â! GPS satellite orbits: precision needed requires GR calculations
â! Gravitational lensing, black holes: astronomical observations confirm
â! Gravitational wave astronomy: see http://www.ligo-la.caltech.edu/LLO/overviewsci.htm
â! Notice: LIGO is a variety of Michelson apparatus!
â˘! Weâre still looking for unexplained anomalies: UW is a center for this work â! See http://www.npl.washington.edu/eotwash/index.html
*âIf relativity is proved right, the Germans will
call me a great German, the Swiss will call me a
great Swiss, and the French will call me a great citizen of the world.
If relativity is proved wrong, the French will call
me a Swiss, the Swiss will call me a German,
and the Germans will call me a Jew.â -Einstein
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Worldlines for the twin paradox
â˘! Diagram shows worldlines for the twins
â! Notice travelling twin has to jump from going to coming = acceleration!
â! This means travelling twin observes an apparent jump in age of his twin between arrival and departure from star
â˘! In relativity there is no absolute âright nowâ â! Events that are simultaneous in one frame may occur at different times in another*
â! Lines of simultaneity are tilted according to relative speed
* For more details on simultaneity, see http://en.wikipedia.org/wiki/Relativity_of_simultaneity
Spacetime diagram (in rest frame) of
âsimultaneousâ events for two observers,
2nd has v=0.25c relative to 1st
v = 0.25c
At rest Note: we assume earth
and star are at rest
relative to one another!
Starâs
worldline
Event in rest frame occurs at
different time in moving frame
From each spacetime point in the rest frame we can
draw a âline of simultaneityâ for the moving frame
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Blackbody radiation: another 1890s puzzle
â˘! Any objectâs molecules are vibrating in place
âŚAs long as its temperature is above âabsolute zeroâ : 0° K = - 273° C
â˘! Atoms are made of charged particles
â! So they emit E-M radiation
â! Frequency of emission depends on motion
â! Total radiation from any object covers a broad range of frequencies (wavelengths): random mix of molecular speeds
â˘! Calculated spectrum (graph of intensity vs wavelength) from an ideal radiator is called âblackbody spectrumâ
â! Ideal radiator = ideal radiation absorber
â! Color of an object = color of light it reflects (does not absorb)
â˘! So, what color would an ideal absorber appear to be?
Experimental approximation for a blackbody
Metal cavity with pinhole: any light that enters is unlikely to escape before walls absorb its energy
~ perfect absorber
âRed hotâ glass
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âBlackbodyâ Spectrum (Planck Spectrum) BB=object with 100% efficient emission and absorption at any wavelength
Spectrum = graph of how
much energy at each wavelength
Blackbody spectrum features: Higher temperature means:
1.! More total energy (=area
under curve): ETOT ! T4 2.!Peak is at shorter
wavelength (bluer color)
Kelvin temperature scale: uses Celsius-
size degrees, but
measures from
absolute zero:
0 C = +273 K
physics.weber.edu/palen/Phsx1040/images/blackbody.jpg Visible: 400â800 nanometer
Examples:
Surface of Sun = 6000K
Carbon arc = 4000K
Light bulb = 3000K
IR UV
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Classical prediction doesnât match observations
â˘! According to Maxwellâs equations and 1890s thermodynamics, emission
intensity should rise rapidly with frequency â any real BB would have to emit infinite total energy (= area under spectrum curve)
â˘! âUltraviolet catastropheâ!
â˘! W. Wien (1896):
â˘! Max Planck (Germany, 1901):
Found an empirical formula that
approximates observations
Found he could match
observations precisely if he made a simple assumption:
suppose atoms can emit energy only in units (âquantaâ)
with size depending on
frequency:
Planckâs constant: very tiny on human scale!
Closer look: Taking the temperature of the Universe
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Spectrum of radiation from âempty spaceâ matches the Planck BB spectrum for 2.725 deg K very precisely
(error bars are tiny compared to dots: about 0.05 units)
The cosmic microwave background (CMB)
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â˘! Sky map of the Cosmic Microwave Background (from NASAâs WMAP satellite - âequatorâ = plane of our Galaxy)
Each dot = measured temperature in that direction on the sky â˘! Color range from red to dark blue = a variation of only + 0.0002 degrees K from 2.75K average temperature! â˘! Even these tiny variations are meaningful: fluctuations represent origins of galaxies!
Sky map: same idea
as map of the world, but looking up at
stars, not down on Earth.
Here, âequatorâ =
Galactic Plane (our galaxy = Milky way)
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First observed by Heinrich Hertz in 1887 - explained by
Albert Einstein in 1905.
The Photoelectric Effect
Ammeter Battery
light
Vacuum tube
Flow of electrons =
current
Demonstration in class:
â˘!Charge up an electroscope â˘! Bright light discharges it
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Einsteinâs explanation
â˘! Letâs take Planckâs quantum idea seriously! (sound familiar?)
â! Not just a math trick that fixes up the blackbody spectrum puzzle
â˘! Suppose energy in the form of light really does come in quanta?
â! Planck said: violet light quanta have more E than red quanta
Planckâs law: E = h f = h c/! ! red light = long wavelengths, violet = short
â! Quantum concept means energy is delivered in bundles, not continuously, as with waves
â! Electrons cannot âsoak upâ energy: each photon (Einsteinâs new term for quanta or âparticlesâ of light) transfers a lump of energy all at once
â! Only short ! photons carry enough energy per quantum to knock an electron loose (negative charges had been identified as electrons by Thompson)
â! Long ! photons can never kick electrons loose: too little E/photon
â! Intense light means many photons but not more energy per photon!
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Photons kick out
electrons via
photoelectric effect Photocathode: metallic salt
coating on inside of glass tube
Each energetic
electron ejects
about 4 new
electrons at each
âdynodeâ stage Vacuum inside tube
Multiplied signal
comes out here
A + voltage
between
dynodes makes
electrons accelerate
from stage to stage
Photomultiplier Tube: application of photoelectric effect
â˘! Crucial device for medical imaging, basic research
â˘! Can detect single photons of UV light
â˘! Photonâs arrival time determined to nanosecond accuracy
â˘! One photon in can be multiplied to produce millions of electrons out: easily measured signals
High + voltage
attracts and
accelerates
photoelectrons
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Photomultipliers = everyday technology
â˘! Every time we use one, we prove Einstein was rightâŚ
1â diameter PMT
Array of hexagonal 2â PMTs used in medical imaging
â˘! If I stand still on Earth, and you go past me in a spaceship moving with v = 0.99c
A.!I say your clock runs slow relative to mine
B.!You say my clock runs slow relative to yours
C.!Both of the above are true
D.!Neither A nor B are true
Quiz for today