Download - Wave / Particle Duality
Page 1
Wave / Particle Duality PART I
• Electrons as discrete Particles.– Measurement of e (oil-drop expt.) and e/m (e-beam expt.).
• Photons as discrete Particles.– Blackbody Radiation: Temp. Relations & Spectral Distribution.
– Photoelectric Effect: Photon “kicks out” Electron.
– Compton Effect: Photon “scatters” off Electron.
PART II
• Wave Behavior: Diffraction and Interference.
• Photons as Waves: = hc / E – X-ray Diffraction (Bragg’s Law)
• Electrons as Waves: = h / p = hc / pc– Low-Energy Electron Diffraction (LEED)
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• In the late 1800’s, scientists discovered that electricity was composed of discrete or quantized particles (electrons) that had a measurable charge.
• Found defined amounts of charge in electrolysis experiments, where F (or Farad) = NA e.
– One Farad (96,500 C) always decomposes one mole (NA) of monovalent ions.
• Found charge e using Millikan oil-drop experiment.
• Found charge to mass ratio e/m using electron beams in cathode ray tubes.
Electrons: Quantized Charged Particles
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Charged oil droplets
Charged Plates
Scope to measure droplet terminal velocity.
Electrons: Millikan’s Oil-drop Expt.
• Millikan measured quantized charge values for oil droplets, proving that charge consisted of quantized electrons.
– Formula for charge q used terminal velocity of droplet’s fall between uncharged plates (v1) and during rise (v2) between charged plates.
2
1
1vmg
qE v
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Electron Beam e/m : Motion in E and B Fields
Electron (left hand)
B
vBF
Proton (right hand)
E eF E
B e F v B
2
( ) ( )centrip B
mvor evB or
rmv m
reB e
F F
Circular Motion of electron in B field:
B
vBF
Larger e/m gives smaller r, or larger deflection.
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Electron Beam e/m: Cathode Ray Tube (CRT)
J.J. Thomson
Cathode (hot filament
produces electrons)
Charged Plates(deflect e-beam)
Slits(collimate beam) Fluorescent Screen
(view e-beam)
• Tube used to produce an electron beam, deflect it with electric/magnetic fields, and then measure e/m ratio.
• Found in TV, computer monitor, oscilloscope, etc.
(+) charge
(–) charge
Deflection e/m
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Ionized Beam q/m: Mass Spectrometer
• Mass spectrometer measures q/m for unknown elements.
2 21 2
2
qVmv qV v
m
2 2
2q V
m B R
1.
2.
2 2 22
2 2 2 2
2
mvR
qB
m v m qVR
q B q B m
1.
2.
Ions accelerated by E field.
Ion path curved by B field.
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Photons: Quantized Energy Particle
• Light comes in discrete energy “packets” called photons.
From Relativity:
For a Photon (m = 0):
2222 mcpcE
pcEpcE 022
1240
( )
eV nmhcE hf
nm
Rest mass
Energy ofSingle Photon
E hc hp
c c Momentum of
Single Photon
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Photons: Electromagnetic Spectrum
Fre
quen
cy
Wav
elen
gth
Visible Spectrum
400 nm
700 nm
Gamma Rays
X-Rays
Ultraviolet
Infrared
MicrowaveShort Radio Waves
TV and FM Radio
AM Radio
Long Radio Waves
Visible
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Photoelectric Effect: “Particle Behavior” of Photon
PHOTON IN ELECTRON OUT
• Photoelectric effect experiment shows quantum nature of light, or existence of energy packets called photons.
– Theory by Einstein and experiments by Millikan.
• A single photon can eject a single electron from a material only if it has the minimum energy necessary (or work function – For example, if 1 eV is necessary to remove an electron from a
metal surface, then only a 1 eV (or higher energy) photon can eject the electron.
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Photoelectric Effect: “Particle Behavior” of Photon
PHOTON IN ELECTRON OUT
• Electron ejection occurs instantaneously, indicating that photons cannot be “added up.”
– If 1 eV is necessary to remove an electron from a metal surface, then two 0.5 eV photons cannot add together to eject the electron.
• Extra energy from the photon is converted to kinetic energy of the outgoing electron.
– For example above, a 2 eV photon would eject an electron having 1 eV kinetic energy.
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Photoelectric Effect: Apparatus
Light
Cathode
Anode
• Electrons collected as “photoelectric” current at anode.
• Photocurrent becomes zero when retarding voltage VR equals stopping voltage Vstop, i.e. eVstop = Ke
• Photons hit metal cathode and eject electrons with work function .
• Electrons travel from cathode to anode against retarding voltage VR
(measures kinetic energy Ke of electrons).
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• Total photon energy =e– ejection energy + e– kinetic energy.
– where hc/ = photon energy, = work function, and eVstop = stopping energy.
• Special Case: No kinetic energy (Vo = 0).– Minimum energy to eject electron.
Photoelectric Effect: Equations
2
2 stop
hc mveV
minmin
hcE
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Photoelectric Effect: IV Curve Dependence
Intensity I dependence
Frequency f dependence
Vstop= Constant
Vstop f
f1 > f2 > f3
f1
f3
f2
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Photoelectric Effect: Vstop vs. Frequency
stopeV hf
min0stopV hf
Slope = h = Planck’s constanthfmin
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Photoelectric Effect: Threshold Energy Problem
21240
2620t t
t
hc eVnmE and
E eVeV nm
( 2 ), 2 2(2 2 2)2 ot
t thc
For or E E eV E eV eV
If the work function for a metal is = 2.0 eV, then find the threshold energy Et and wavelength t for the photoelectric effect. Also, find the stopping potential Vo if the wavelength of the incident light equals 2t and t /2.
At threshold, Ek = eVo = 0 and the photoelectric equation reduces to:
For 2t, the incoming light has twice the threshold wavelength (or half the threshold energy) and therefore does not have sufficient energy to eject an electron. Therefore, the stopping potential Vo is meaningless because there are no photoelectrons to stop!
For t/2, the incoming light has half the threshold wavelength (or twice the threshold energy) and can therefore eject an electron with the following stopping potential:
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Compton Scattering: “Particle-like” Behavior of Photon
• An incoming photon (E1) can inelastically scatter from an electron and lose energy, resulting in an outgoing photon (E2) with lower energy (E2 < E1
• The resulting energy loss (or change in wavelength ) can be calculated from the scattering angle
Anglemeasured
ScatteringCrystal
Incoming X-ray Scattered X-ray
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Compton Scattering: Schematic
11
hcE
PHOTON IN PHOTON OUT (inelastic)
22
hcE
22
hcE
