R. J. Wilkes

Email: ph116@u.washington.edu

Physics 116

Session 30 Blackbody radiation and the photoelectric effect

Nov 18, 2011

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

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Lecture Schedule (up to exam 3)

Today

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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

–! 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

*“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

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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

* For more details on simultaneity, see http://en.wikipedia.org/wiki/Relativity_of_simultaneity

Spacetime diagram (in rest frame) of

“simultaneous” 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!

Star’s

worldline

Event in rest frame occurs at

different time in moving frame

From each spacetime point in the rest frame we can

draw a “line of simultaneity” for the moving frame

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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

•! 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

“Red hot” glass

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“Blackbody” 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: 400—800 nanometer

Examples:

Surface of Sun = 6000K

Carbon arc = 4000K

Light bulb = 3000K

IR UV

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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):

•! 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 (“quanta”)

with size depending on

frequency:

Planck’s constant: very tiny on human scale!

Closer look: Taking the temperature of the Universe

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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)

The cosmic microwave background (CMB)

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•! 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)

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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:

•!Charge up an electroscope •! Bright light discharges it

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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!

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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

“dynode” 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

•! Crucial device for medical imaging, basic research

•! Can detect single photons of UV light

•! Photon’s arrival time determined to nanosecond accuracy

•! 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

•! Every time we use one, we prove Einstein was right…

1” diameter PMT

Array of hexagonal 2” PMTs used in medical imaging

•! 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