Physics 1C Lecture 28B
"In quantum mechanics we have found a
region of the universe where the human brain is simply unable to be comfortable."
--James Trefil
http://jewishcurrents.org/december-14-quantum-indeterminacy-judaism-13377
Outline Last time:
Blackbody radiation - Planck’s solution
(1918 Nobel Prize)
Photoelectric effect - Einstein’s theory
(1921 Nobel Prize)
Today:
Compton effect (1927 Nobel Prize)
Quantum Dots
Nature’s Use of Quantum Mechanics
Photoelectric Effect
Key ideas from the photoelectric effect:
Light of frequency f consists of individual, discrete
quanta, each of energy E = hf. These quanta are
called photons.
In the photoelectric effect, photons are emitted or
absorbed on an all-or-nothing basis.
A photon, when absorbed by a metal, delivers it’s
entire energy to a single electron. The light’s energy
is transformed into electron kinetic energy.
The energy of a photon is independent of the
intensity of light.
KEmax hf
The Compton Effect In 1923, Arthur Compton (U of Chicago) directed a
beam of x-rays toward a block of graphite
He detected that some of the scattered x-rays had
a slightly longer wavelength than the incident x-
rays.
This means those scattered photons had less
energy than the incident photons.
The amount of energy those scattered photons lost
depended on the angle at which the x-rays were
scattered.
This change in wavelength is called the Compton
shift (1927 Nobel Prize).
The Compton Effect To calculate the shift in wavelength, Compton
assumed that the photons act like other particles in
collisions.
In the collisions, energy, hf, and momentum, hf/c,
were conserved. The energy of
the incoming
photon was:
After it collides it
scatters by an
angle θ.
The Compton Effect
0.00243e
hnm
m c
After the collision the photon has an energy:
The wavelength shift becomes:
where the
Compton
wavelength for
the electron is a
constant:
' 1 coso
e
h
m c
The Compton Effect Schematic diagram of Compton’s apparatus:
The x-ray spectrometer includes a crystal that reflects
x-rays and an ionization chamber that measures I.
An x-ray tube
produces
radiation of
o = 0.0707nm
that strikes a
carbon target.
Angle is
varied by
moving the x-
ray source.
The Compton Effect The wavelength of the scattered x-rays
can be determined from the angle at
which they were reflected from the crystal
with maximum intensity (x-ray diffraction).
The graphs show the spectra of scattered
x-rays for various angles .
The shifted peak at ’ is caused by the
scattering of free electrons in the target:
The unshifted wavelength, o, is due to
x-rays scattered from the electrons that
are tightly bound to the target atoms.
' 1 coso
e
h
m c
The Compton Effect It demonstrates that light cannot be explained purely
as a wave phenomenon.
Compton's experiment convinced physicists that
light can behave as a stream of particle-like objects
(quanta) whose energy is proportional to the
frequency.
Interaction between electrons and high energy
photons results in the electron being given part of
the energy (making it recoil), and a photon
containing the remaining energy
so that the overall momentum of the system is
conserved.
How can we use Quantum
behavior?
Does nature use quantum
behavior?
If so, how?
Quantum Dots: Artificial
Atoms
http://www.invitrogen.com
12
Summary: Standing Waves in
the Box
0
5
10
15
20
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
Rel
ativ
e E
ner
gy
x
n = 1
n = 2
n = 3
n = 4
L
Confined electrons exist
as standing waves,
whose energies take on
discrete values
Quantum Dots: Artificial
Molecules
O OH
OO
CH3
aspirin R = radius of the nanoparticle
Michael J. Sailor, UC San Diego
Felice Frankel
“Artificial atoms” made from
CdSe in solution
Bawendi research group, MIT
6 nm 2 nm 3 nm 2.5 nm 5 nm 4 nm
The properties of a nanomaterial derive from its size—
form determines function
Biological Applications of Quantum Dots
Advantages: Stable
Many Distinct Colors
"Semiconductor nanocrystals as fluorescent biological labels." Bruchez, M.; Moronne,
M.; Gin, P.; Weiss, S.; Alivisatos, A. P. Science 1998, 281, 2013-2016.
84 microns
Mouse 3T3 fibroblasts
simultaneously stained with
red and green quantum dots
Applications: Biological Staining
Drug Discovery
Genomics
Silicon quantum dots imaging a tumor in a mouse
Nature’s Use of Quantum
Mechanics We discussed how the sun’s spectrum is that of a
blackbody – due to discrete energy levels
Light
Chemical Energy
In what other manner does nature
use quantum mechanics?
Photosynthesis –
natural absorption of
light
Vermaas “An Introduction to Photosynthesis
and Its Applications”
Nature’s Use of Quantum
Mechanics
Plants
Algae
Cyanobacteria
Prokaryotic
photosynthetic
bacteria
James D. Johnson M.S.
Alumnus, Department of Chemistry
Florida State University, Tallahassee, FL, USA
The Photosynthetic Apparatus
Light Harvesting
(Antennae)
Reaction Center
Photosynthetic Bacteria
Carotenoids
Natural version of the quantum dot
For Next Time (FNT)
Chapter 28 readings and Homework
due Wednesday by class time