The Wave – Particle Duality

OR

Light Waves

Until about 1900, the classical wave theory of light describedmost observed phenomenon.

Until about 1900, the classical wave theory of light describedmost observed phenomenon.

Light waves:

Characterized by:

Amplitude (A) Frequency () Wavelength ()

Energy A2

And then there was a problem…

However, in the early 20th century, several effects were observed which could not be understood using the wave theory of light. So other experiments were done and found it could behave as both::

1) The Photo-Electric Effect (particle)

2) The Compton Effect (particle)

3) Taylor’s experiment (wave)

4) DeBroglie Wavelength (wave)

Quantized Model of Light (Photons)

• In 1900 Max Planck proposed that light energy comes in packets (quanta) spread at random on a wave front called PHOTONS. • He even doubted his idea since:

It went against wave theory by saying that electromagnetic waves don't transmit energy continuously but in small packets.It went against Newtonian physics since objects aren't free to vibrate with any energy. The energy only has certain discreet values.

Quantized Model of Light

Energy of a light particle (Photon):

h = 6.6x10-34 [J*sec]

Planck’s constant, after the scientist Max Planck

photon

hcE hf

The Electromagnetic Spectrum

Shortest wavelengths(Most energetic photons)

Shortest wavelengths(Most energetic photons)

Longest wavelengths(Least energetic photons)

Longest wavelengths(Least energetic photons)

hcE hf

Photons

Problems:1.Find the energy in electron volts (eV)  for a quantum of orange light with frequency 5.00 x 1014 Hz. (Answer: 2.07eV)

2.Find the energy in electron volts for a quantum of yellow light with a wavelength of 580 nm. (Answer: 2.14 eV) Suggested Textbook Problems:Page 597 #2-6

Vary wavelength, fixed amplitude

electrons emitted ?

What if we try this ?

Photoelectric Effect

No electrons were emitted until the frequency of the light exceeded a threshold frequency, at which point electrons were emitted!

No

Yes, withlow KE

Yes, withhigh KE

Increase energy by increasing amplitude

“Classical” Method

electrons emitted ?

No

No

No

No

of

PhotoelectricElectrons are attracted to the (positively charged) nucleus by theelectrical force

In metals, the outermost electrons are not tightly bound

If given energy electrons can be freed

Classically, we increase the energyof an EM wave by increasing theintensity (e.g. brightness)

Energy A2

But this doesn’t work ??But this doesn’t work ??

PhotoElectric Effect

An alternate view is that light is acting like a particle

The light particle (photon) must have enough energy to “free” the electron

Increasing the Amplitude is just simply increasing the numberof light particles, but its NOT increasing the energy of each one!

However, if the energy of these “light particle” is related to their frequency, this would explain why higher frequency light canknock the electrons out of their atoms, but low frequency light cannot…

An alternate view is that light is acting like a particle

The light particle (photon) must have enough energy to “free” the electron

Increasing the Amplitude is just simply increasing the numberof light particles, but its NOT increasing the energy of each one!

However, if the energy of these “light particle” is related to their frequency, this would explain why higher frequency light canknock the electrons out of their atoms, but low frequency light cannot…

Photo-Electric Effect

“Light particle”

Metal Surface

• See diagram below …the energy of thelight particle (photon) must overcome the binding energy of the electron to the nucleus (Work)

• Ephoton = Ek + Work.

• Ek = Ephoton – Work. (Einstein’s Photoelectric Equation)

• See diagram below …the energy of thelight particle (photon) must overcome the binding energy of the electron to the nucleus (Work)

• Ephoton = Ek + Work.

• Ek = Ephoton – Work. (Einstein’s Photoelectric Equation)

“Freed” electron has Ek

Work to free elctron

Photo-Electric Problems1. EM radiation of frequency 7.0 X 1014 Hz falls on a

metal with work function of 0.5eV.      a) Calculate the maximum kinetic energy of the

emitted photoelectrons and the maximum speed of the emitted photoelectrons.

        (Answer: 3.8 x 10 –19 J)        NOTE: Remind students if questions ask for

speed make sure you convert everything into Joules.

    b) What would be the case if the kinetic energy was less than 0.5 eV. (Answer: no emission)

Photo-Electric Problems2. Calculate the Threshold (minimum) frequency for a

metal with a work function or binding energy of 1.5 eV. (Answer: 3.6 x 1014)

3. A photoelectric surface has a work function of 1.50 eV.  A red light of wavelength 650 nm is directed at the surface. Calculate:a) The maximum Ek of the emitted photoelectrons in joules (Answer: 6.60 x 10 -20 J)b) The photoelectrons' maximum speed (Answer:  3.81 x 10 5 m/s)c) The cutoff potential needed to stop the photoelectrons (Answer: 0.412 V)

Photo-Electric ProblemsSuggested Text Questions:

Pg. 604 #10-15

The Compton Effect1924 Compton performed the photoelectric exp with X-rays .Like the photoelectric effect it showed light behaving as a particle.

MATTER

Incident X-ray1

Scattered X-ray2

e

Electron comes flying out

The Compton Effect

'xray photon xray photon k electronE E E

Notice: There is NO work function since it is negligible (compared to x-ray energy).

Energy and momentum are conserved

The Compton Effect

Compton derived the expression for momentum of a photon. 2

2photon

photon

photon

photon

E mc

E mc

Emc

chf

pch

p

hp

Bohr’s Complementarity

Principle

If light is passing through a medium treat it like a wave.

If light is reacting with matter treat it as a particle.

Wave Nature of Matter

DeBroglie thought: “If light waves can behave like a particle, might particles act like waves”?

DeBroglie’s wavelength: h h

p mv

Matter Waves (cont)

Ex 1: Compute the wavelength of a 1 [kg] block moving at 1000 [m/s].

= h/mv = 6.6x10-34 J s/(1kg)(1000 m/s) = 6.6x10-37 [m].

VERY small. therefore wave behavior of matter can’t be seen.

Electron Microscope

This image was taken with a Scanning Electron Microscope (SEM).

These devices can resolve features downto about 1 [nm]. This is about 100 times better than can be done with visible light microscopes!

This image was taken with a Scanning Electron Microscope (SEM).

These devices can resolve features downto about 1 [nm]. This is about 100 times better than can be done with visible light microscopes!

The electron microscope is a device which uses the wave behavior of electrons to make images which are otherwise too small using visible light!

IMPORTANT POINT HERE:High energy particles can be used to reveal the structure of matter !

High Energy ParticlesHigh energy particles can provide a way to reveal the structure of matter beyond what can be seen using an optical microscope.

The higher the momentum of the particle, the smaller thedeBroglie wavelength.

As wavelength decreases, finer and finer details about thestructure of matter are revealed !

This is done at facilities often referred to as “atom-smashers” or “accelerators”

High energy particles can provide a way to reveal the structure of matter beyond what can be seen using an optical microscope.

The higher the momentum of the particle, the smaller thedeBroglie wavelength.

As wavelength decreases, finer and finer details about thestructure of matter are revealed !

This is done at facilities often referred to as “atom-smashers” or “accelerators”