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!