Transcript Lecture 5 - Stanford University

Lecture 9
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 (‘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.
An 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
Traveling wave description
E y ( x, t )  Eo sin(kx  t )
k=wavevector
c=ω/k = λν
Intensity of light wave = energy flowing per unit area per second
1
2
I  c oE o
2
From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)
Young’s Double Slit Experiment
http://www.youtube.com/watch?v=DfPeprQ7oGc
x
d
L
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
being "reflected" by various atomic planes in the crystal.
Bragg’s Law
Bragg diffraction condition
2d sinθ  nλ
n  1, 2, 3, ...
The 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
crystal 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.
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
This work comes from the electrons kinetic energy just after
photoemission
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
eVo=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 the light intensity.
Results: Kinetic energy & light frequency
The effect of varying the frequency of light and the cathode material in the
photoelectric experiment. The lines for the different materials have the
same slope h but different intercepts
Photoelectric Effect
Photoemitted electron’s maximum KE is KEm
KEm  h  h0
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
Light Intensity (Irradiance)
Classical light intensity
Light Intensity
1
2
I  c oE o
2
I  ph h
Photon flux (# photons crossing a unit area per unit time)
ph 
N ph
At
X-rays are photons
X-ray image of an American one-cent coin captured using an x-ray a-Se HARP camera.
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
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, Revisited
What happens when we observe which slit the
photon goes through?
x
d
L
http://www.youtube.com/watch?v=DfPeprQ7oGc