Chapter 27- Photoelectric Effect

- Wave/Particle Duality

- Heisenberg Uncertainty Principle

First discovered by Hertz in 1887 (as a side notein an experiment which demonstrated the wavenature of light as hypothesized by Maxwell), thephotoelectric effect could only be explained by aparticle model of light!

V+

_ V

A

A

C evacuatedchamber

With monochromatic light of an appropriatefrequency incident upon the photocathode,a current is detected in the ammeter.

The existence of a current indicates thatwhen the light strikes the plate, charges arebeing released!

-6 -4 -2 0 2 4 6 8 10

Applied Voltage

Cu

rren

t

High intensity

Low intensity

Stopping potentia

l

1) The magnitude of the current depends uponthe intensity of the light source.

2) As the applied voltage increases, the currentincreases until the point at which all freedelectrons are being captured by the anode.

-6 -4 -2 0 2 4 6 8 10

Applied Voltage

Cu

rren

t

High intensity

Low intensity

Stopping potentia

l

3) A current will flow for voltages greater thanthe stopping potential.

4) The existence of a current depends only uponthe applied voltage and the frequency of theincident light, NOT the intensity of that light.

If you now were to plot the stopping potentialas a function of the frequency of the incidentradiation...

frequencyfc

stop

pin

gp

oten

tial

cutoff frequency

These observations contradicted the classicaltheory, which suggested that the current shouldexist for any frequency of light, so long as theintensity of the light was strong enough...

Recall, the potential energy of a charge in anelectric field is simply qV. In this case, thestopping potential represents the maximumpotential difference the electron can cross. So,

KEmax = e Vo

When you fire the ball into thegravel, rocks will fly out. Theharder you throw the ball, thefaster the rocks fly away.

This analogy illustrates the classical expectationfor the interaction of light with the electrons inthe metal during the photoelectric experiment.

But this model is inconsistentwith the observations!

Einstein extended Planck’s concept of energyquantization to electromagnetic waves (light).

In particular, Einstein proposed that lightactually consisted of a stream of particlesknown as “photons.” Being electromagneticwaves, however, each photon has a character-istic wavelength and frequency. The energy ofa photon, according to Einstein, is given by

E = h f

Einstein also hypothesized the following:

Electrons struck by photons incident upon the metal surface must pass through the surface to be freed and conduct electricity across the gap. This barrier is a characteristic of the metal itself and is described as the work function of the metal. As a result, freed electrons will have a maximum kinetic energy given by

KE hfmax energy of theincident light

Energy requiredto escape the metal

With this theory, Einstein successfully explainedall the observations associated with the photoelectric effect experiment. He received the Nobel Prize in 1921 for this work.

Among other things, you have Einstein tothank for our ability to hear the soundtrackat the movie theater!

(The edge of movie film contains a strip withvarying lights and darks. Light from theprojector passes through this strip, illuminatinga photo cell. The frequencies of this illuminationcan be directly translated into audible sound!)

Which you may have already noticed implicitlyin our explanation of the photoelectric effect.

Light is both a wave and a particle!

Photoelectric Effect

Light as a PARTICLE.

Young’s Experiment

Light as a WAVE.

Sometimes, light acts like a particle;other times, light acts like a wave.

It turns out (and it’s not too hard toconvince yourself) that the shorter thewavelength of the light, the more thelight acts like a particle and the lessit acts like a wave.

High frequency

More energy

More similarto a particle

“Okay, so let’s assume that light is botha particle and a wave. If that’s true,perhaps all matter has both particle andwave characteristics.”

This was exactly the hypothesis ofLuis de Broglie in his 1924 dissertation!

De Broglie extended Einstein’s theory tocover all matter, not just photons!

According to Einstein, a fundamentalrelationship exists between energy andmomentum:

E pc

(We’ll cover this in more detail when wetalk about relativity.)

Here, p is the momentum and c the speed of light.

As we saw in the photoelectric effect, Einstein demonstrated that the energy of a photon of light was related to its frequency:

E = h f

Combining the two, we find a relationshipbetween the momentum of a photon andits frequency:

h f pc

Recall that c = f , so we can expressmomentum as a function of wavelength:

ph

de Broglie’s hypothesis was that anyparticle with momentum p should alsoexhibit wave properties with characteristicwavelength .

The momentum of a macroscopic particleis given by….

p mv

mvh

So

which means h

mv

What is the de Broglie wavelength of a 60 kg person jogging at 5 m/s?

h

mv

6 626 10

60

34.

( )(5 )

Js

kg m / s

2 21 10 36. m

Obviously, we’re never going to observethe diffraction of our jogger!

But before we discount de Broglie’shypothesis entirely, let’s take a lookat another example...

What is the de Broglie wavelength of an electron moving at 2.2 X 106 m/s?

h

mv

6 626 10

9 1 10 2 2 10

34

31 6

.

( . )( . )

Js

kg m / s

0 332. nm

This is a scale at which diffraction effects mayactually be observed...

Also notice that the slower the electrontravels, the longer the de Brogliewavelength will be!

One last great mystery...

It’s 1927…and Werner Heisenberg iswondering to himself (as you undoubtedlyare now), “Just how well can you knowand define a physical system?”

Well, what’s there to know?

vm

x

Mass times velocity is momentum

position

The two quantities which define a system

How well can we know these two quantites?

Classically, there are no limits to ourmeasurement precision and accuracy.We can know them both perfectly!

Quantum physicstells us otherwise!

Afterall, how is it that we becomeaware of the characteristics ofa physical system?

Through observation!

In order to make an observation,LIGHT must be involved!

And light can have an impact on matter,changing the momentum and or energyof the system we’re observing!

(As we’ve seen in the photoelectric effectand as covered in the text on the Comptoneffect.)

So by observing the system,we necessarily change the system!

The process of observing introducesuncertainties in the physical quantitieswhich characterize the system.

If we describe the uncertainty in themomentum of the system as p and theuncertainty in the location of the systemas x, Heisenberg tells us that the uncertainty in these quantities must satisfy the expression...

x ph

4

Which says that it is impossible to knowboth the position and momentum of aparticle with infinite accuracy.