Photoelectric Effect & Blackbody Radiation - Brown University
Transcript of Photoelectric Effect & Blackbody Radiation - Brown University
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Gaitskell
PH0008Quantum Mechanics and Special Relativity
Lecture 02 (Quantum Mechanics)
020402v1
Photoelectric Effect& Blackbody Radiation
Prof Rick Gaitskell
Department of PhysicsBrown University
Main source at Brown Course Publisher
background material may also be available at http://gaitskell.brown.edu
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Section: Quantum Mechanics Week 1
START OF WEEK
• Homework (due for M 4/1)o [SpecRel] Done
• I will return Exam I on Friday
THIS WEEK
• Reading (Prepare for 4/1)
o SpecRel for Exam• Revise Ch2-6 (look at Ch 1 also)
o QuantMech• Ch1,2 & 3
• Lecture 01 (M 4/1)o Quantum Mechanics
• Introduction
• Photoelectric Effect Demo
• Lecture 02 (W 4/3)o Quantum Mechanics
• Photoelectric Effect
• Blackbody Radiation
• Lecture 03 (F 4/5)o Quantum Mechanics
• Atomic Line Spectra
• Bohr Atom
NEXT WEEKEND
• Reading (Prepare for 4/8 after recess)
o SpecRel• Revise
o QuantMech• Ch1,2 & 3
• No Homework (M 4/8)o Revision for Exam (M4/8)
• Homework #9 (M 4/15)o (see web “Assignments”)
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Question SectionQuestion Section
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Question Quant Mech L02-Q1
•What is Planck’s constant … a constant of directproportionality between which two properties of aparticle…?
o(1) Energy and Wavelength
o(2) Momentum and Wavelength
o(3) Energy and Frequency
o(4) Momentum and Frequency
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Classical Physics in CrisisClassical Physics in Crisis
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
The Birth of Modern Physics
• Experiments that were at odds with Classical Model of Physics (around1900)
o Problems for both Newtonian physics, and purely wave theory of light
• Those we will considero Photoelectric Effect
o Blackbody Radiation
o Atomic Line Spectra
• Further experiments that study QM effectso Davisson-Germer (1925)
• Electron (30-600 eV) scattering from surface of single crystal metal
o GP Thomson (1927)• Electron (10-40 keV) transmission through micro-crystalline foils
o Double Slits - Single Photons (1909…)
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
The Great Grand-daddy ofThe Great Grand-daddy ofThe CrisesThe Crises
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Blackbody (thermal) RadiationBlackbody (thermal) Radiation
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Definition of Blackbody Radiation
• Consider a box with all walls at a given temperature
• Outside:o The spectrum of electromagnetic radiation given off by the outside is dependent onthe material that the box is made of…
• Inside:o It is a result of thermodynamics (empirically tested) that the spectrum of radiationinside the box is independent of the material of the walls
• This spectrum is know as blackbody spectrum.
• It would be characteristic of an object which was a perfect absorber, and so a perfectemitter as well…
—A good example is a hole in a box!
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Normal Models in Cavity (Box)
• Consider Electromagnetic Waves in Cavity (box)o The standing waves have zero amplitude at walls - this looks like are previous normal mode
analysis…
• 1-D Standing waves can be established with nl / 2 = Lo Classically there is NO limit to how short the wavelength can become
• There is no limitation due to “medium” (no aether); EM-Maxwell doesn’t have a length scale
o Each Normal mode is a “degree of freedom”• A result of classical physics is that at equilibrium each degree of freedom will contain the same
amount of energy (thermodynamics tells us Eper dof~kBT, where kB is known as the Boltzmannconstant)…
• …this creates a problem because there are an infinite number of normal modes… most of them withvery small wavelengths…(we get more normal modes per dl interval)
• … the Radiancy R( l) is the power in spectrum per unit area per unit wavelength bin dl
o Extrapolate this to all 3 dimensions…
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Blackbody Spectrum Observed vs Rayleigh-Jeans
5500 K
4000 K
Wavelength l [nm]
Rad
ianc
y R
( l)
[Wcm
-2nm
-1]
Rayleigh-Jeans Theory (dashed) Derived from Classical EM & Thermodynamics R( l) ~ l –4
Note: Classical theory does agree with observation at long wavelengths But, rapid divergence as l->0
Observed Blackbody Spectra at two different temperatures
<- Ultraviolet Catastrophe ! (shorter wavelengths)
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Resolving Crisis: The beginning…• Planck 1900
o Suggest that “if” it is assumed that energy of normal mode is quantised such that E=hn (h isan arbitrary constant, Planck’s arbitrary constant, experimentaly determined so that theoryfits data) then higher frequency (shorter wavelength) modes will be suppressed/eliminated.
o Planck suggests ad hoc that the radiation emitted from the walls must happen in discretebundles (called quanta) such that E=hn . Mathematically this additional effect generates anexpression for spectrum that fits data well.
• The Planck constant is determined empirically from then existing data• The short wavelength modes are eliminated
o In a classical theory, the wave amplitude is related to the energy, but there is no necessarylink between the frequency and energy
• Classically one can have low freq. waves of high energy and vise versa without constraint• Planck is unable to explain how such an effect could come about in classical physics
• Einstein 1905o Based on Photoelectric effect, Einstein proposed quantisation of light (photons)
• Photons are both emitted and absorbed in quanta
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Photoelectric EffectPhotoelectric Effect
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
––
Experimental Setup (1)
• Illumination of Photoelectric material in vacuum
o Electromagnetic waves couple to electrons• Ejecting some of them from material if they are given sufficient energy to overcome
binding into material (known as “work function”)
• Ejected electrons have a range of Kinetic Energies
–
V
Photoelectric Material
I
2nd Electrode
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Experimental Setup (2)
• +ve bias on sense electrode
o Bias accelerates electron toward sense plate
–
V
Photoelectric Material
I
2nd Electrode
+ –
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
• –ve bias on sense electrode
o Voltage raised to the a level where Potential overcomes Kinetic Energy of ejectedelectron
• Current measured falls to zero
Experimental Setup (3)
–
V
Photoelectric Material
I
2nd Electrode
+–
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
• Response to different incoming wave intensitieso (Note that this turns out to be wrong…)
Experimental Setup (4) - Classical Interpretation
–
V
Smaller KE
I
2nd Electrode
– Larger KE
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
• Response to different incoming wave intensities - apply –ve bias
o Voltage raised to the a level where Potential overcomes Kinetic Energy of ejectedelectron
• Current measured falls to zero, we can use the Voltage as an Energy Spectrometer
Experimental Setup (5) - Classical Interpretation
–
V
Smaller KE
I
2nd Electrode
– Larger KE
+–
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
• Voltage as an Energy Spectrometer - apply –ve bias
Experimental Setup (6) - Electron Potential Diagram
–
V
Smaller KE
I
2nd Electrode
– Larger KE
+–
+ –
PotentialEnergy
of electron
Increasing KE elec
-V0
I1 I2 > I1
–
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PH0008 Gaitskell Class Spring2002 Rick Gaitskell
Light Sources
• Filters - approximate band-passo Red 600-700 nm
o Green 520-600 nm
o Blue 450-550 nm
Visible Wavelength Spectrum from http://imagers.gsfc.nasa.gov/ems/visible.html
Wavelength 700nm 600nm 500nm 400nm