Physics 116
Session 30
Blackbody radiation and
the photoelectric effect
Nov 18, 2011
R. J. Wilkes
Email: ph116@u.washington.edu
Announcements:
•! Updated quiz score totals will be posted on WebAssign tomorrow
•! Nice series on PBS covering topics we will discuss in class:
Brian Greene’s Fabric of the Cosmos
http://www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.html
Lecture Schedule
(up to exam 3)
Today
3
General relativity
•! Einstein, 1915: extended relativity to accelerated frames: general relativity
–! GR really describes the geometry of spacetime: gravity of massive objects warps
spacetime in their vicinity
–! Equivalence Principle: Observations cannot distinguish a uniformly accelerated
frame from a uniform gravity field
–! Eddington, 1919: GR predictions matched observed anomalies in orbit of
Mercury, Newtonian predictions do not – Einstein is right*
•! More predictions and consequences of GR:
–!
–!
–!
–!
Gravitational time dilation and redshift
Deflection of light by gravity
Gravitational waves
Black holes
•! Applications confirming GR today
*“If 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.” -Einstein
–! GPS satellite orbits: precision needed requires GR calculations
–! Gravitational lensing, black holes: astronomical observations confirm
–! Gravitational wave astronomy: see http://www.ligo-la.caltech.edu/LLO/overviewsci.htm
–! Notice: LIGO is a variety of Michelson apparatus!
•! We’re still looking for unexplained anomalies: UW is a center for this work
–! See http://www.npl.washington.edu/eotwash/index.html
4
Worldlines for the twin paradox
•! Diagram shows worldlines for the twins
–! Notice travelling twin has to jump from going to coming = acceleration!
–! This means travelling twin observes an apparent jump in age of his twin
between arrival and departure from star
•! In relativity there is no absolute “right now”
–! Events that are simultaneous in one frame may occur at different times in another*
–! Lines of simultaneity are tilted according to relative speed
Spacetime diagram (in rest frame) of
“simultaneous” events for two observers,
2nd has v=0.25c relative to 1st
Event in rest frame occurs at
different time in moving frame
v = 0.25c
At rest
From each spacetime point in the rest frame we can
draw a “line of simultaneity” for the moving frame
Star’s
worldline
Note: we assume earth
and star are at rest
relative to one another!
* For more details on simultaneity, see http://en.wikipedia.org/wiki/Relativity_of_simultaneity
5
Blackbody radiation: another 1890s puzzle
•! Any object’s molecules are vibrating in place
…As long as its temperature is above “absolute zero” : 0° K = - 273° C
“Red hot” glass
•! Atoms are made of charged particles
–! So they emit E-M radiation
–! Frequency of emission depends on motion
–! Total radiation from any object covers a broad range of frequencies
(wavelengths): random mix of molecular speeds
•! Calculated spectrum (graph of intensity vs wavelength) from an
ideal radiator is called “blackbody spectrum”
–! Ideal radiator = ideal radiation absorber
–! Color of an object = color of light it reflects (does not absorb)
•! 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
6
“Blackbody” Spectrum (Planck Spectrum)
BB=object with 100% efficient emission and absorption at any wavelength
Kelvin temperature
scale: uses Celsiussize degrees, but
measures from
absolute zero:
0 C = +273 K
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)
Visible: 400—800 nanometer
UV
IR
Examples:
Surface of Sun = 6000K
Carbon arc = 4000K
Light bulb = 3000K
physics.weber.edu/palen/Phsx1040/images/blackbody.jpg
7
Classical prediction doesn’t match observations
•! According to Maxwell’s equations and 1890s thermodynamics, emission
intensity should rise rapidly with frequency – any real BB would have to
emit infinite total energy (= area under spectrum curve)
•! “Ultraviolet catastrophe”!
•! W. Wien (1896):
Found an empirical formula that
approximates observations
•! Max Planck (Germany, 1901):
Found he could match
observations precisely if he
made a simple assumption:
suppose atoms can emit
energy only in units (“quanta”)
with size depending on
frequency:
Planck’s constant: very tiny on human scale!
8
Closer look: Taking the temperature of the Universe
Spectrum of radiation from “empty space” matches the
Planck BB spectrum for 2.725 deg K very precisely
(error bars are tiny compared to dots: about 0.05 units)
9
The cosmic microwave background (CMB)
•! Sky map of the Cosmic Microwave Background (from NASA’s WMAP
satellite - “equator” = plane of our Galaxy)
Each dot = measured temperature in that direction on the sky
•! Color range from red to dark blue = a variation of only + 0.0002
degrees K from 2.75K average temperature!
•! 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, “equator” =
Galactic Plane (our
galaxy = Milky way)
10
The Photoelectric Effect
First observed by Heinrich Hertz in 1887 - explained by
Albert Einstein in 1905.
light
Vacuum tube
Ammeter
Battery
Flow of electrons =
current
Demonstration in class:
•! Charge up an electroscope
•! Bright light discharges it
11
Einstein’s explanation
•! Let’s take Planck’s quantum idea seriously! (sound familiar?)
–! Not just a math trick that fixes up the blackbody spectrum puzzle
•! Suppose energy in the form of light really does come in quanta?
–! Planck said: violet light quanta have more E than red quanta
Planck’s law: E = h f = h c/! ! red light = long wavelengths, violet = short
–! Quantum concept means energy is delivered in bundles, not
continuously, as with waves
–! Electrons cannot ‘soak up’ energy: each photon (Einstein’s new term
for quanta or ‘particles’ of light) transfers a lump of energy all at once
–! Only short ! photons carry enough energy per quantum to knock an
electron loose (negative charges had been identified as electrons by
Thompson)
–! Long ! photons can never kick electrons loose: too little E/photon
–! Intense light means many photons but not more energy per photon!
12
Photomultiplier Tube: application of photoelectric effect
Photocathode: metallic salt
•! Crucial device for
coating on inside of glass tube
medical imaging,
basic research
•! Can detect single
photons of UV light
•! Photon’s arrival time
determined to
nanosecond accuracy Each energetic
•! One photon in can be electron ejects
4 new
multiplied to produce about
electrons at each
“dynode” stage
millions of electrons
out: easily measured
signals
Multiplied signal
comes out here
Photons kick out
electrons via
photoelectric effect
High + voltage
attracts and
accelerates
photoelectrons
Vacuum inside tube
A + voltage
between
dynodes makes
electrons accelerate
from stage to stage
13
Photomultipliers = everyday technology
•! Every time we use one, we prove Einstein was right…
1” diameter PMT
Array of hexagonal 2” PMTs
used in medical imaging
14
Quiz for today
•! 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