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Lecture 7Lecture 7
Quantum Mechanics (made fun and easy)
Why the world needs quantum mechanics
Why the world needs quantum mechanics
Why the world needs quantum mechanics
Why the world needs quantum mechanics
Why the world needs quantum mechanics
Why the world needs quantum mechanics
Quantum Mechanics in Action
CdS (‘ d i ll ’)CdS (‘cadmium yellow’)CdS nanocrystal
2 nm
Quantum Weirdness: The Zeno Effect
Quantum Weirdness: superposition of states
Quantum Weirdness: superposition of states
Quantum Weirdness: superposition of states
Light as a particle (Newton, 1643-1727)
Light as a Wave (1861: Maxwell)
The classical view of light as an electromagnetic wave.l l h l dAn electromagnetic wave is a traveling wave with time-varying electric and
magnetic fields that are perpendicular to each other and to the direction of propagation.
Light as a wave
)i ()( tkt EETraveling wave description
)sin(),( tkxtx oy EEk=wavevector
c=ω/k = λν
Intensity of light wave = energy flowing per unit area per second
2
21
oocI E
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
2
Young’s Double Slit Experiment
htt // t b / t h? DfP Q7 Ghttp://www.youtube.com/watch?v=DfPeprQ7oGc
x
Ld
Schematic illustration of Young’s double-slit experiment. Constructive interference occurs when nλL=xd
X-ray Diffraction
X-ray diffraction involves constructive interference of waves ybeing "reflected" by various atomic planes in the crystal.
Bragg’s Law
Bragg diffraction conditionBragg diffraction condition
321sin2 nnλθd ...3,2,1, sin 2 nnλθd
Th ti i f d t B ’ l d i f thThe equation is referred to as Bragg’s law, and arises from the
constructive interference of scattered waves.
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw‐Hill, 2005)
X-ray Diffraction
Diffraction patterns obtained by passing X-rays through crystals can only be explained by using ideas based on the interference of waves. (a) Diffraction of X-rays from a single
l d ff f b h h h f l (b) ff fcrystal gives a diffraction pattern of bright spots on a photographic film. (b) Diffraction of X-rays from a powdered crystalline material or a polycrystalline material gives a
diffraction pattern of bright rings on a photographic film.
The Photoelectric Effect (1921 Nobel Prize)
Illuminate cathode and monitor generated current as a function of applied voltage
Results: Photocurrent versus voltage & intensity
Photocurrent
Photoelectric current vs. voltage when the cathode is illuminated with light of identical wavelength but different intensities (I).
The saturation current is proportional to the light intensity
Results: Photocurrent versus voltage & wavelength
Photocurrent
The stopping voltage and therefore the maximum kinetic energy of the emitted electron increases with the frequency of
light ν. g
Interpretation I:
When an electron traverses a voltage difference V, it’s potential energy changed by eV.
When a negative voltage is applied to the anode, the electron has to do work to get to this electrode
h k f h l k fThis work comes from the electrons kinetic energy just after photoemission
Wh th ti d lt V i l t V hi h j t When the negative anode voltage V is equal to Vo, which just “extinguishes” the current I, the potential energy gained by the electron balances the kinetic energy lost by the electron
eV 1/ mv2 KEeVo=1/2mv2=KEm
Interpretation II:
Photocurrent
Since the magnitude of the saturation photocurrent depends on the light intensity, only the number of ejected electrons depends
on th light int n it on the light intensity.
Results: Kinetic energy & light frequency
The effect of varying the frequency of light and the cathode material in the y g q y gphotoelectric experiment. The lines for the different materials have the
same slope h but different intercepts
Photoelectric Effect
Photoemitted electron’s maximum KE is KEm
hhKE 0 hhKEm
Work function, F0
The constant h is called Planck’s constant.
First full interpretation: 1905, Einstein
The PE of an electron inside the metal is lower than outside by an energy called the workfunction of the metal. Work must be done
to remove the electron from the metal.
Ø=hc/eλo, where λo is the longest wavelength for photoemission
Photoelectric effect: Light is a particle with energy
Red photons – no current; blue photons – measured currentLight = energy packets (photons) with energy E=hνPhotoemission only occurs when E > workfunction Øy Ø
Ø=hc/eλo, where λo is the longest wavelength for photoemission Work function of a metal keeps the electron in the material
Light Intensity (Irradiance)
Classical light intensity 21 cI EClassical light intensity2 oocI E
hI phLight Intensity
Photon flux (# photons crossing a unit area per unit time)
tAN
ph
ph
X-rays are photons
X-ray image of an American one-cent coin captured using an x-ray a-Se HARP camera. Th fi i h l f i b i d d l l d h The first image at the top left is obtained under extremely low exposure and the
subsequent images are obtained with increasing exposure of approximately one order of magnitude between each image. The slight attenuation of the X-ray photons by Lincoln provides the image. The image sequence clearly shows the discrete nature of x-rays, and p g g q y y ,
hence their description in terms of photons.SOURCE: Courtesy of Dylan Hunt and John Rowlands, Sunnybrook Hospital, University
of Toronto.
Quantum Weirdness II: Young’s Double Slit Experiment, Revisitedp
What happens when we observe which slit the photon goes through?p g g
d
x
Ld
http://www.youtube.com/watch?v=DfPeprQ7oGc
Compton effect: Light also has momentum
1927 Nobel prizeHolly Compton found that X-ray wavelengths increase due to ray wavelengths increase due to scattering of the photon by free electrons in the material f h d hfurther demonstrates the particle nature of light
Compton’s experiment and results
Compton’s experiment and results
Compton scattering
Scattering of an X-ray photon by a “free” electron in a conductor. g y p ySince the electron has a momentum, by conservation of momentum, the x-ray must also have momentum.
h' hhKEm
hp
Summary equations: light as a particle & wave
hEEnergy:
2
kWavevector:
h
khp
Momentum:
202
1 EchI Intensity: 02y
The solar spectrum
Ab i b H d
Ab i b
Absorption by H and He in the sun
Absorption by molecules in the
atmosphere
What causes the overall shape?
Blackbody radiationBlackbodies absorb all electromagnetic radiationgAppear black when coldAs they heat up, begin to emit radiationColor depends on temperature – the hotter the Color depends on temperature the hotter the temperature, the higher the emitted photon energy
Blackbody radiation (1900, Max Planck)
S h i ill i f bl k b d di iSchematic illustration of black body radiation
Blackbody radiation
Classical theory
Planck’s radiation law
Spectral irradiance vs. wavelength at two temperatures (3000K is p g p (about the temperature of the incandescent tungsten filament in a light
bulb.)
Classical Theory (“Rayleigh-Jeans law”)
Thermal vibrations and rotations give rise to radiated electromagnetic waves that will interfere with each other,
i i i di l i i h giving rise to many standing electromagnetic waves in the “oven”
Each standing wave contributes ~kT of energy (from kinetic molecular theory)
By calculating the number of standing waves, find irradience
Iλ ~ T ~ 1/λ4Iλ ~ T ~ 1/λ
Planck’s Theory
Assumed radiation in oven involved emission and absorption of discrete amounts of light energy by the oscillation of
l lmolecules.
Assumed the probability of a molecule (an oscillator) possessing an energy nhν (n an integer) was proportional to
the Boltzmann factor (think kinetic molecular theory)
2 2
hchcI
1exp5
kThc
Stefan’s Law
Integrating the irradiance over all wavelengths yields the total radiated power PS emitted by a blackbody per unit surface area
Tat a temperature T:
4TP TP SS
452 k
Stefan’s constant
42832 K m W 10670.5
152
hck
S
Stefan’s law for real surfacesElectromagnetic radiation emitted from a hot surfaceg
Pradiation = total radiation power emitted (W = J s-1)
][ 40
4radiation TTSP S ][ 0radiation S
σS = Stefan’s constant, W m-2 K-4
ε = emissivity of the surface
ε = 1 for a perfect black body p yε < 1 for other surfaces
S = surface area of emitter (m2)
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw‐Hill, 2005)
S surface area of emitter (m )
Temperature of a lightbulb filament
100 Watt lightbulbgemissivity ε=0.35.
Filament length of 57.9cm, diameter of 31 7 i31.7 microns.
S=2π(31 7x10-6m)(0 579m)=1 15 x 10-4m2S=2π(31.7x10 m)(0.579m)=1.15 x 10 m
Ps=100 W =SεσS(TF4-T0
4)s S( F 0 )T0=300K
TF=2573 K = 2300o C
A h f bl kb d i h k i i
Wein’s displacement law
As the temperature of a blackbody increases, the peak emission shifts to shorter wavelengths: λ*T=2.89x10-3 m*K
Cl ssic l theoryClassical theory
Planck’s radiation law
The solar spectrum
Ab i b H d
Ab i b
Absorption by H and He in the sun
Absorption by molecules in the
atmosphere
What causes the overall shape? Blackbody emission at ~6000K!