Modern PhysicsModern PhysicsQuantum EffectsQuantum Effects

1773 – 1829

ObjectivesObjectives

Explain the Explain the photoelectric effectphotoelectric effect and and recognize that quantum theory can explain recognize that quantum theory can explain it, but wave theory cannotit, but wave theory cannot

Explain the Explain the Compton effectCompton effect, and describe , and describe it in terms of the momentum and energy of it in terms of the momentum and energy of a photona photon

Modern physicsModern physics

Microscopic realmMicroscopic realmAtoms and subatomic particlesAtoms and subatomic particles

Classical Physics (Newtonian)Classical Physics (Newtonian)

Macroscopic objectsMacroscopic objectsMarbles to moonsMarbles to moonsPendulums to planetsPendulums to planetsSprings to starsSprings to stars

Classical PhysicsClassical Physics

Debate over light and matterDebate over light and matter Isaac Newton – beam of particlesIsaac Newton – beam of particles Christian Huygens – wave theory Christian Huygens – wave theory Observed phenomenaObserved phenomena

• ReflectionReflection• RefractionRefraction• InterferenceInterference• DiffractionDiffraction

Electric charge was once thought to be a fluid“Phlogiston,” a substance released by combustion“Luminiferous aether,” a medium for transporting light

Maxwell’s EquationsMaxwell’s Equations

E

EB

tB

c BE

t

j

0

2

0

0

= electric charge density

j = electric current density

= permittivity of free space0

1831 – 1879

Heinrich HertzHeinrich Hertz““The wave theory of light is, from The wave theory of light is, from

the point of view of human beings, the point of view of human beings, a certainty”a certainty”

1857 – 1894

Properties of Light and MatterProperties of Light and Matter

LightLight frequencyfrequency wavelengthwavelength energyenergy

• amplitudeamplitude• intensityintensity

continuouscontinuous velocityvelocity

• v = λƒ = cv = λƒ = c• v = 3x10v = 3x1088m/s m/s

MatterMatter massmass momentummomentum energyenergy

• potentialpotential• kinetickinetic

discretediscrete velocityvelocity

• v v c c

Disaster Strikes!Disaster Strikes!

Wave Theory Can’t ExplainWave Theory Can’t Explain

Blackbody RadiationBlackbody Radiation

Objects absorb certain colors (wavelengths) and Objects absorb certain colors (wavelengths) and reflect othersreflect others

Objects that are heated glow with different colors Objects that are heated glow with different colors related to their temperaturerelated to their temperature

An ideal “blackbody” absorbs all incident light, An ideal “blackbody” absorbs all incident light, and emits radiation based only on its and emits radiation based only on its temperaturetemperature

Classical wave mechanics can’t explain the Classical wave mechanics can’t explain the distribution of wavelengths given off by a distribution of wavelengths given off by a blackbody blackbody

TB Pg. 626

Photoelectric EffectPhotoelectric Effect Electrons are emitted when light strikes Electrons are emitted when light strikes

certain metallic surfacescertain metallic surfaces Interaction starts immediately (no “absorption” Interaction starts immediately (no “absorption”

time)time) Only occurs when light waves reach a certain Only occurs when light waves reach a certain

minimum frequencyminimum frequency Kinetic Kinetic energyenergy of electrons increases with of electrons increases with

frequencyfrequency of the light wave of the light wave NumberNumber of electrons is proportional to the of electrons is proportional to the

intensityintensity of the light of the lightTB Pg. 628

From a Wave PerspectiveFrom a Wave Perspective

Electrons require energy to break their molecular Electrons require energy to break their molecular bondsbonds

Energy of a wave is related to its intensity Energy of a wave is related to its intensity (brightness)(brightness)

Low intensity light of any frequency might take Low intensity light of any frequency might take longer to be absorbed, but should still worklonger to be absorbed, but should still work

High intensity should give electrons more energyHigh intensity should give electrons more energy Kinetic energy (velocity) of the electrons should Kinetic energy (velocity) of the electrons should

increase with the intensity of the lightincrease with the intensity of the light

Laws of Photoelectric EmissionLaws of Photoelectric Emission I. The rate of emission of photoelectrons I. The rate of emission of photoelectrons

is directly proportional to the intensity of is directly proportional to the intensity of incident lightincident light

II. The kinetic energy of photoelectrons is II. The kinetic energy of photoelectrons is independent of the intensity of the incident independent of the intensity of the incident lightlight

III.III. The maximum kinetic energy of The maximum kinetic energy of photoelectrons varies directly with the photoelectrons varies directly with the difference between the frequency of the difference between the frequency of the incident light and the cutoff frequencyincident light and the cutoff frequency

Photoelectric EffectPhotoelectric Effect

Impossible to explain with Impossible to explain with wavewave mechanicsmechanics

Light is behaving like a Light is behaving like a particleparticle

Photoelectric EffectPhotoelectric Effect

Binding energy of the electron Binding energy of the electron is related to the wave is related to the wave frequency & Planck’s constantfrequency & Planck’s constanthh = Planck’s constant = Planck’s constant

• = 6.63 x 10= 6.63 x 10-34-34 joule·secondjoule·second

Work FunctionWork Function

Minimum energy needed to free an Minimum energy needed to free an electronelectron

where fwhere f00 = the threshold frequency = the threshold frequency

Kinetic energy of the electron (K = Kinetic energy of the electron (K = ½½mvmv22))

W = hf0

K = hf hf0

TB Pg. 630

QuantizationQuantization

Energy is “Energy is “quantizedquantized”” Specific amount required (“all or Specific amount required (“all or

nothing”) to free the electronnothing”) to free the electron Any additional energy increases the Any additional energy increases the

velocity (kinetic energy) of the electronvelocity (kinetic energy) of the electron Light and other forms of radiation Light and other forms of radiation

consist of discrete bundles of energyconsist of discrete bundles of energy Called “photons”Called “photons”

Light is QuantizedLight is Quantized

““Quantized” means light comes in Quantized” means light comes in discretediscrete bundles, rather than a bundles, rather than a continuouscontinuous spectrum spectrum ““Discreteness” is the essence of a Discreteness” is the essence of a

particleparticle Light behaves as a particle when it Light behaves as a particle when it

interacts with electronsinteracts with electrons A different way of A different way of lookinglooking at light! at light!

Quantized QuantitiesQuantized Quantities We live in a quantized universe (integral We live in a quantized universe (integral

multiples)multiples) MassMass AtomsAtoms ChargeCharge

• Elementary charge (±1.60 x 10Elementary charge (±1.60 x 10-19-19C)C) EnergyEnergy

• Radiation emitted or absorbedRadiation emitted or absorbed• Fundamental quantity (Fundamental quantity (hfhf))

Compton EffectCompton Effect

X-rays bombarding graphiteX-rays bombarding graphite Arthur Holly Compton, 1922Arthur Holly Compton, 1922 Electrons ejected from graphiteElectrons ejected from graphite Scattered X-rays had a longer Scattered X-rays had a longer

wavelength than the incident energywavelength than the incident energy Energy and momentum gained by the Energy and momentum gained by the

electrons equal the energy and electrons equal the energy and momentum lost by the X-ray photonsmomentum lost by the X-ray photons

TB Pg. 635

QuestionQuestion

Which results in photoelectrons with more Which results in photoelectrons with more energy, a dim blue light or a bright red energy, a dim blue light or a bright red light?light?

TB Pg. 632

PracticePractice

A photon has 2.11 electronvolts of energy. A photon has 2.11 electronvolts of energy. What is the energy in joules? What is its What is the energy in joules? What is its frequency and color? (1eV = 1.6 x 10frequency and color? (1eV = 1.6 x 10-19-19 J) J)

Given:E = 2.11 eVh = 6.63 x 10-34 J·sE = hf

Find:E = ? (J)f = ? (Hz)color = ?

AnswerAnswer

E eVx J

eV

E x J

fE

h

x J

x J s

f x Hz

color yellow

FHG

IKJ

211160 10

1

338 10

338 10

6 63 10

510 10

19

19

19

34

14

..

.

.

.

.

Given:E = 2.11 eVh = 6.63 x 10-34 J·sE = hf

Find:E = ? (J)f = ? (Hz)color = ?

PracticePractice

The threshold wavelength of sodium is The threshold wavelength of sodium is 536 nm.536 nm. What is the work function of sodium in eV?What is the work function of sodium in eV? If ultraviolet radiation with a wavelength of If ultraviolet radiation with a wavelength of

348 nm falls on sodium, will electrons be 348 nm falls on sodium, will electrons be ejected, and if so, and what is their energy in ejected, and if so, and what is their energy in eV?eV?

AnswerAnswer

Find the work function using Planck’s Find the work function using Planck’s constant and constant and 00

0

00

536

1240

536

2 31

nm

W hfhc eV nm

nm

W eV.

AnswerAnswer

Use Einstein’s photoelectric equation to Use Einstein’s photoelectric equation to find the energy of the electronfind the energy of the electron

E hfhc eV nm

nmE eV

K hf hf eV eV

K eV

1240

346356

356 2 31

1250

.

. .

.