Today

The Photo Electric Effect(Part 2)

Summary from last class

The photoelectric effect:Light shines on metal.à Electrons are emitted.

Is it just a heating effect?

http://phet.colorado.edu

Last class: We found that electrons come out of the metal plate when we shine light on it.

Measure the current!

0 Battery Voltage

Curr

ent

Each electron that pops out is accelerated and hits the plate on the right side.

BUT: # of electrons = constantsec

So current is constant!

What’s happening here?

reverse V,no electronsflow.

Similar V-I curve as a vacuum tube diode!

not I = V / R !!

Here, electrons are repelled by neg. electrode

We found an interesting current vs. voltage curve

Swimming Pool AnalogyIf no water slops over side of pool, no flow. Little pump or big pump, still no water current.If electrons stuck inside metal plate, no current for little or big V.

Pump(Battery)

Pool party: put bunch of energy into water, splash some out,get flow through pump.Put energy into metal by heating it very hot,gives electrons energy, some “splash” out. Gives current.

?

Pump(Battery)

q

What do you think does actually happen?

Current I

Voltage U

Optical power P- frequency f

Now: Take out a piece of paper and draw the following graphs with what you expect will happen.)

1. Current vs. Voltage with the lamp on (fixed color, say UV light, and fixed intensity.)

2. Current vs. Frequency (color) at a fixed intensity and voltage (right plate is on positive potential)

3. Current vs. Intensity for fixed color (right plate is at fixed, positive voltage)

http://phet.colorado.edu

Let's do the ‘experiment’!

Measure the current!

Play with color and intensity. Measure current I. (I ~ #e-/s)

photoelectric_en.jar photoelectric online

That's what happened:

0 U

I

1. Current vs. Voltage:

0 Frequency

I

2. I vs. f:

0 Frequency

Init

ial K

E

or: Initial KE vs. f:

0 Intensity

I

3. I vs. intensity:

low intensityhigh intensity

Threshold

Threshold Threshold

0 Batt. V

I

0 Batt. V

0 Batt. V

I

0 Batt. V

I

Which graph best represents low and high intensity curves for a fixed color of the light?

0 Batt. V

I

A B

C D

E

photoelectric_en.jar

I

Predict what happens to the initial KE of the electrons as the frequencyof light changes? (Light intensity is constant)

Predict shape of the graph

I

e’s

0 Frequency of light

Init

ial K

E

0 Frequency

Init

ial K

E

0 FrequencyIn

itia

l KE

0 Frequency

Init

ial K

E

0 Frequency

Init

ial K

E

A B

C D

E. something different

I

e’s

0 Frequency of light

Init

ial K

E As the frequency of light increases (shorter λ!), the KE of electrons being popped out increases.(it is a linear relationship)

There is a minimum frequency below which the light could not kick out electrons… even if we wait a long time

Correct answer is D.

What about different metals?(try sim) photoelectric_en.jar

Ekin,max=hf - φ

Review: PE sim. That's what we found:

0 U

I1. Current vs. Voltage:

0 Frequency

I

2. I vs. f:

0 Frequency

Init

ial K

E

or: Initial KE vs. f:

0 Intensity

I

3. I vs. intensity:

low intensityhigh intensity

Threshold

Threshold Threshold

What did we observe so far?• Color doesmatter! The velocity (and

number) of the electrons seems to increase with frequency (fUV > fblue > fred)

• Positive voltage does not affect current (at fixed color and intensity).

• Large negative voltages make current go to zero; but never observe negative current.

• Frequency and negative voltage show ‘threshold’ behavior. (Need f > fthreshold)

Questions? photoelectric_en.jar

Remember definition of 'eV'

EF

-U0V

path

----

Define electron-volt (eV):1eV = kinetic energy gained (or lost) by an electron when

accelerated (decelerated) through 1 volt of potentialdifference

à The lowest negative voltage required to stop the current multiplied by the electron charge qe corresponds to the initial kinetic energy of the fastest electrons! This lowest voltage is called the stopping potential.

photoelectric_en.jar

I

e’s

0 Battery Voltage

I

Voltage to turn aroundmost energetic electron:“stopping potential”

photoelectric_en.jar

I

e’s

HIGH intensity

0 Battery Voltage

I

Low intensity: fewer electrons pop out off metal à Current decreases.Current proportional to light intensity.

LOW intensity

Same initial kinetic energy. à same “stopping potential”.

Summary of PE experiment results

1. Current linearly proportional to intensity.

2. Current appears with no delay.

3. Electrons only emitted if frequency of light exceeds a threshold.

4. Maximum kinetic energy with which electrons come out increases linearly with frequency but does not depend on intensity.

5. Threshold frequency depends on type of metal.

how do these compare with classical wave predictions?

Classical wave predictions vs. experimental observations

• Increase intensity à current increases.Experiment matches with classical prediction

•Takes time to heat up ⇒ if thermal effect, current would initially be low and increase with time.Experiment: electrons come out immediately, no time delay to heat up

•Classical: Color of light does not matter, only intensity.Experiment shows strong dependence on color

•Current vs. voltage: step close to zero Volts, then flat.Flat part matches to classical pred., but experiment has 'tail' of energetic electrons à Stopping potential, which depends on color (not only intensity).

What could it be?

The PE effect is inconsistent with classical E&M theory!!

PE effect: Discovered 1887 by Hertz, 1905 Explained by Einstein, using some of Plank's ideas. Nobel prize: 1921

“…”

Einstein proposed: "…the energy in a beam of light is not distributed continuously through space, but consists of a finite number of energy quanta, which are localized at points, which cannot be subdivided, and which are absorbed and emitted only as whole units." He took the energy of these single units to be hf, as proposed earlier by Planck.

Doesn’t look like a wave to me… Seems more like a particle!!

Is light a stream of particles?Yes! Also….

E = hf

Ekin,max=hf - φ

“Work function” (I’ll explain later)

The energy of a photon is E = hfThe wavelength of a photon is λ = c/f = hc/E The momentum of a photon is p = E/c = hf/c The mass of a photon is m = 0

h ≈ 6.626 ·10-34 J·s: Plank constant

It sometimes is useful to define h = h/(2π)The energy of a photon is then: E = hf = hω

Properties of photons

The frequency of a beam of light is decreased but the light’s intensity remains unchanged. Which of the following is true?

A. There are more photons per second but each photon has less energy.

B. There are more photons per second and each photon has more energy.

C. There are fewer photons per second and each photon has less energy.

D. There are fewer photons per second but each photon has more energy.

E. Nothing happens to the photon number because light is a wave.

Photons

The minimum amount of energy needed to free an electron from a piece of metal is called the

a. Gibb’s free energy.b. quantum energy.c. liberation potential.d. work function. e. threshold energy.

What actually happens in the metal when a photon strikes?

Why do the emitted electrons have different velocities/kinetic energies?

What determines the work function ‘Φ’?

What happens in the metal? Kicker analogy:Photon is like a kicker in a pit… Puts in energy. All concentratedon one ball/electron.Blue kicker has a fixed strength.

KE = kick energy - mghBall emerges with:

mgh = energy needed to make it up hill and out.mgh for highest electronanalogous to work function.

Fixed kick energy:Top ones get out……bottom ones don’t.

h

metal

electrons

Red kicker (photon) kicks less than blue one. Nothing gets out.

‘Photon’ ‘Electron’ For electrons: KE = hf - Φ

Φ

Different metals à different ‘pit depths’

sodium- easy to kick out

platinum, hard to kick outlarge work function ⇔ deep pit

Φ

small work function ⇔ shallow pit

Φ

PE effect: Apply Conservation of Energy

Inside metal

Ele

ctro

n P

oten

tial

Ene

rgy

work function (Φ) = energy needed to kickhighest electron out of metal

Energy of photon = energy needed to kick KE of electronelectron out of metal as it exits the metal

Loosely stuck electron, takes least energy to kick out

Tightly stuck, needs more energy to escape

Outside the metal

Energy in = Energy out

Φ

Energy in = Energy out

+

“Fermi” level (weakest bound electron)

Q:Electrons over large range of energy have about equal chance of absorbing photons.

Insidemetal

Ele

ctro

n po

tent

ial

ener

gySay you shine blue light on a metal plate à the metal emits n electrons per sec.

work function ΦEphot

Ephot

a. fewer electrons / sec.b. same # of electrons/sec but electrons are fasterc. more electrons/sec. d. not enough informatione. no change because light is a wave

Now you change the frequency to violet light without changing the # of photons per second.

What happens to the number of electrons/sec. coming out of the metal?

Electrons over large range of energy have equal chance of absorbing photons.

metalPot

entia

l ene

rgy

of e

lect

rons

work function ΦEphot

c. more electrons come out with violet

absorb blue light and have enough energy to leaveabsorb blue light, but don’t come out

so the more energy the light has, the more electrons that comeout, until so much energy that every electron comes out.(violet and ultraviolet would not be very different in this case)

photoelectric_en.jar

Typical energiesEach photon has: Energy = Planks constant * Frequency

(Energy in Joules) (Energy in eV)E=hf=(6.626*10-34 J-s)*(f in Hz) E=hf= (4.14*10-15 eV-s)*(f in Hz)E=hc/λ = (1.99*10-25 J-m)/(λ m) E= hc/λ = (1240 eV-nm)/(λ nm)

Photon Energies:

Work functions of metals (in eV):Aluminum 4.08 eV Cesium 2.1 Lead 4.14 Potassium 2.3Beryllium 5.0 eV Cobalt 5.0 Magnesium 3.68 Platinum 6.35Cadmium 4.07 eV Copper 4.7 Mercury 4.5 Selenium 5.11Calcium 2.9 Gold 5.1 Nickel 5.01 Silver 4.73Carbon 4.81 Iron 4.5 Niobium 4.3 Sodium 2.28

Uranium 3.6Zinc 4.3

Red Photon: 650 nm Ephoton = 1240 eV-nm = 1.91 eV650 nm

Application of the PE effect:The photo multiplier tube (PMT)

Electron