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