Wave-Particle Duality

Light quanta revisitedand introduction to matter

waves

Review of Diffraction

• When of wave is larger than obstacle/slit then more diffraction occurs

• If of wave is small, you need a small obstacle/slit to observe diffraction

• To diffract X-rays (very short ), you need obstacles/slits the scale of atoms in crystals

• Long light diffracts easily (passes around) the molecules in the air, whereas short light is easily scattered - thus the blue sky and red/orange sunset/sunrise

When short light (why not long ?) interacts with free charges (not bound to atoms), momentum and energy must be conserved. By giving some of its energy to the charge, the photon’s frequency ________, while its ________.

Momentum is conserved separately in x- and -y dimensions.

Young’s Double-slit experiment with light

• Demonstrated that light was wave• Interference pattern produced;

diffraction occurred: > distance between slits produced

greater diffraction• Waves can interfere with one

anotherLINK

But… what about

•Blackbody spectrum•Photoelectric effect

These phenomena proved that light comes in packets (“quanta” or “photons”)… so, what’s the deal?

deBroglie Matter Waves

• Since light exhibits particle-like behavior, perhaps matter could exhibit wave-like behavior…

p

h

h is Planck’s constant and p is momentum

Davisson-Germer

• Scattering a beam of electrons off of nickel target

• Accident caused nickel to crystallize• Diffraction of the electron beam

was observed – of electron “wave” much smaller than visible light, so need very small spacing of crystal “slits” for diffraction

LINK

Light vs. Electron microscopes

• Light microscopes are limited by the of visible light. If object is smaller, waves diffract around it and it can’t be seen

• Electron waves are much, much shorter than visible light waves, so they can resolve much smaller objects

Summary

• Waves can exhibit particle-like properties– Blackbody spectra– Photoelectric effect– Compton scattering

• Matter can exhibit wave-like properties– Electron diffraction

Reconciliation of the viewpoints

The “wave” for both light and matter is a probability wave… It describes where the photons or electrons are allowed to be…

Where is the

electron in the box?

L

Double-slit experiment for electrons

• When electrons fired toward a slit for which d < , a diffraction pattern is seen

• If current is lowered so that only 1 electron is allowed at a time - pattern is STILL SEEN!

How does the electron “know” where to go?

If method is used to “look” for electron to see

which slit it passed through, the pattern

disappears! You see the two-slit “shadow.” The process of “looking” at the electron interferes with its position and

momentum. It “collapses” the electron probability wave so that

only one possibility exists - not both simultaneously.

If you look

If you don’t