classical / quantum interpretation of their behaviors

DUAL NATURE WAVE/PARTICLE

Santagati Santa – Corso A

Precondition: light

like a wave

Wave is an oscillation that moves outward from a disturbance

Its properties:

property definition symbol SI units

speed distance traveled per second c m/s

amplitude peak height above midline A varies with type of wave

wavelengh peak-to-peak distance ʎ m

frequency number of peaks passing by per second

ν s-1 (called Hertz)

• constructiveinterference:

amplitudes addpeaks, troughs of interfering waves occur in the same positions (waves are in phase )

• destructive interference:

amplitudes cancel

peaks of one wave are in same position as troughs in the other (waves are out of phase)

Interference

Waves and particles pass through an obstacle

• Waves can bend around small obstacles

• Wave widensfrom Single-slit

.

• Particles effuse from Single-slit

Differences between waves and particles

wave behavior particle behavior

waves interfere particles collide

waves diffract particles effuse

waves are delocalized particles are localized

Is the light a stream of particles or a wave?

Thomas Young - 1801

Light passes through two tiny adjacent slits :if the light was composed of particles

• target would be brightest where light passing through the slits overlapped

• target would darken steadily moving away from the overlap region

this was not observed!Young explained the stripes as a combination of diffraction and interference so these interference fringes are a sure sign of wave behavior White areas are peak-peak or trough-trough overlaps (constructive interference) and black areas are peak-trough overlaps ( destructive interference )

Light isn’t an oscillation of atoms because it can

move through vacuum

19° CENTURY- ELECTROMAGNETISM: light is an electromagneticradiation

• Electric and magnetic field are always coupled and oscillate at right angle

• The speed of light was calculated to be around 3x108m/s and it has beendeterminated experimentally

Energy of electromagnetic radiation

Any radiation carries energy through space:

a classical interpretation: higher amplitude means higher energy and brighter light should carry more energy

a quantistic interpretation : an experiment measured the energy carried by an electromagneticwave

«Photoelectric effect»

Shining light on alkali metals knocks electrons out of metal. Red light can't eject any electrons, but blue light can.????

Einstein explanation of photoelectric effect: light like particles

Einstein interpretion of the photoelectric effect (Nobel Prize, 1921):

• maybe light is like a stream of massless particles (called photons)

• brighter light has more photons of the same energy, but blue light has higher energy photons

• frequency-to-energy conversion factor is h (Planck's constant, 6.626×10-34 J/Hz) E=hν

See video cartoon: https://www.youtube.com/watch?v=YQL2Q5ZArjs

The collapsing atom paradox

What's the electron doing in an atom? • electrons within the atom can't be stationary:

• positively charged nucleus will attract the negatively charged electron • electron will accelerate towards the nucleus

• if electrons within the atom move :• moving charges emit electromagnetic radiation • emission will cause electrons to lose energy and spiral into the nucleus • the atom will collapse!

• why don't atoms collapse? • classical physics has no answer! • key: electrons have wave/particle duality

Electrons as WavesDe Broglie hypothesis (Nobel Prize, 1929)

• Both wave and particle nature matter are connected by relationship that applies to photons:

λ= h/p

where p is the momentum of the particle (p = mass times velocity).

experimental evidence of electron wave/particle duality

electron diffractionC. J. Davisson and G. P. Thomson observed interference fringes when electron beams hit crystal surfaces and thin metal films (Nobel Prize, 1937)

Electron diffraction pattern collected from crystalline silicon

Semiconductor Surface

See video cartoon:

Bound electrons have quantized energies

model I: bead on a wire

• kinetic energy of bead can have any value, because velocity can have any value

• bead can be stationary

• bead is equally likely to be found anywhere on the wire

• exact position and velocity of the bead can be known simultaneously

model II: wave on a wire unite wave and bead models using the

De Broglie relation: E= (nh)^2/8mL^2

• there must be a whole number of peaks and troughs on the wire:

n ( λ/2) = L, where:

• n is an integer (1, 2, 3, ... )

• λ is the wavelength

• L is the length of the wire

standing waves have quantized wavelengths

Quantum number

• E depends on an integer n only certain energy states are allowed

• the integer n labels each state: n is a quantum number

Summarizing:

electrons behave like waves bound electrons in atoms and

bound waves have restricted wavelengths molecules have restricted energies

Electron quantized energy level