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General Physics (PHY 2140)

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Lecture 14Lecture 14Modern Physics1. Relativity

Einstein’s General Relativity

2. Quantum PhysicsBlackbody RadiationPhotoelectric EffectX-RaysDiffraction by CrystalsThe Compton Effect

Chapter 26Chapter 26

Chapter 27Chapter 27

Lightning ReviewLightning Review

Relativity Relativity –– consequences consequences •• Time dilation, length contractionTime dilation, length contraction•• Relativistic energy, momentumRelativistic energy, momentum•• Relativistic addition of velocitiesRelativistic addition of velocities 2 21

ptt

v c

ΔΔ =

−2 21pL L v c= −

2 21mvp mvv c

γ≡ =−

21

ad dbab

ad db

v vv v vc

+=

+KE = KE = γγmc2 mc2 –– mc2mc2

Last lecture:

EinsteinEinstein’’s Postulates:s Postulates:For all inertial frames of reference:For all inertial frames of reference:

Velocity of light in Velocity of light in vacuovacuo, c, is the same (~2.998 , c, is the same (~2.998 ×× 101088 m/sm/s).).

The form of the laws of physics (E/M, Mechanics, thermodynamics,The form of the laws of physics (E/M, Mechanics, thermodynamics, etc.) are etc.) are identical.identical.

Problem: relativistic protonProblem: relativistic proton

A proton in a highA proton in a high--energy accelerator is given a kinetic energy of energy accelerator is given a kinetic energy of 50.0 50.0 GeVGeV. Determine . Determine

(a)(a) the momentum and the momentum and (b)(b) the speed of the proton.the speed of the proton.

A proton in a highA proton in a high--energy accelerator is given a kinetic energy of 50.0 energy accelerator is given a kinetic energy of 50.0 GeVGeV. . Determine (a) the momentum and (b) the speed of the proton.Determine (a) the momentum and (b) the speed of the proton.

Given:

E = 50.0 GeV

mc2 = 946.3 MeV

Find:

p = ?v =?

Recall that EE22 = p= p22cc22 + (mc+ (mc22))22. This can be used to solve for p:

( ) ( ) ( )2 2 22 2 2 2E mc mc KE mcp

c c

− + −= =

( ) ( )( )2 2250.9

KE mc KEGeVp cc

+= =

Thus,

Similarly with velocity:

( )222 2

2

2

11

1 1 0.9998

EE mcmcv c

Ev cmc

γ γ= ⇒ = =−

⎛ ⎞= − =⎜ ⎟⎝ ⎠

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Problem: relativistic Problem: relativistic pionpion

The average lifetime of a The average lifetime of a ππ meson in its own frame of reference (i.e., the meson in its own frame of reference (i.e., the proper lifetime) is 2.6 proper lifetime) is 2.6 ×× 1010––88 s. If the meson moves with a speed of s. If the meson moves with a speed of 0.980.98cc, what is , what is

(a)(a) its mean lifetime as measured by an observer on Earth and its mean lifetime as measured by an observer on Earth and (b)(b) the average distance it travels before decaying as measured by athe average distance it travels before decaying as measured by an n

observer on Earth? observer on Earth? (c)(c) What distance would it travel if time dilation did not occur?What distance would it travel if time dilation did not occur?

The average lifetime of a The average lifetime of a ππ meson in its own frame of reference (i.e., the proper meson in its own frame of reference (i.e., the proper lifetime) is 2.6 lifetime) is 2.6 ×× 1010––88 s. If the meson moves with a speed of 0.98s. If the meson moves with a speed of 0.98cc, what is , what is

(a)(a) its mean lifetime as measured by an observer on Earth and its mean lifetime as measured by an observer on Earth and (b)(b) the average distance it travels before decaying as measured by athe average distance it travels before decaying as measured by an observer n observer

on Earth? on Earth? (c) What distance would it travel if time dilation did not occ(c) What distance would it travel if time dilation did not occur?ur?

Given:

v = 0.98 cτp = 2.6 × 10–8 s

Find:

τ = ?d = ?dn =?

Recall that the time measured by observer on Earth will be longer then the proper time. Thus for the lifetime

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2 21.3 10

1p sv c

ττ −= = ×

−

( )( )( )8 70.98 3 10 1.3 10 38md v m s sτ −= = × × =

Thus, at this speed it will travel

If special relativity were wrong, it would only fly about

( )( )( )8 80.98 3 10 2.6 10 7.6mpd v m s sτ −= = × × =

Problem: more spaceshipsProblem: more spaceships……

A spaceship travels at 0.750A spaceship travels at 0.750c c relative to Earth. If the spaceship fires a relative to Earth. If the spaceship fires a small rocket in the forward direction, how fast (relative to thesmall rocket in the forward direction, how fast (relative to the ship) must it ship) must it be fired for it to travel at 0.950be fired for it to travel at 0.950c c relative to Earth?relative to Earth?

A spaceship travels at 0.750c relative to Earth. If the spaceship fires a small rocket in the forward direction, how fast (relative to the ship) must it be fired for it to travel at 0.950c relative to Earth?

Given:

vSE = 0.750 cvRE = 0.950 c

Find:

vRS = ?

Since vES = -vSE = velocity of Earth relative to ship, the relativistic velocity addition equation gives

RE ESRS

RE ES21

v vv v vc

+=

⋅+

( )( )( )

2

0.950 0.7500.696

0.950 0.7501

c cc

c cc

+ −= = +

−+

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Mass Mass –– Inertial vs. GravitationalInertial vs. Gravitational

Mass has a gravitational attraction for other Mass has a gravitational attraction for other massesmasses

Mass has an inertial property that resists Mass has an inertial property that resists accelerationacceleration

FFii = m= mii aaThe value of G was chosen to make the values The value of G was chosen to make the values of mof mgg and mand mii equalequal

2

'gg

g rmm

GF =

EinsteinEinstein’’s Reasoning s Reasoning Concerning MassConcerning Mass

That mThat mgg and mand mii were directly proportional were directly proportional was evidence for a basic connection was evidence for a basic connection between thembetween themNo mechanical experiment could No mechanical experiment could distinguish between the two massesdistinguish between the two massesHe extended the idea: no experiment of He extended the idea: no experiment of any type can distinguish the two massesany type can distinguish the two masses

Postulates of General RelativityPostulates of General Relativity

All laws of nature must have the same All laws of nature must have the same form for observers in any frame of form for observers in any frame of reference, whether accelerated or notreference, whether accelerated or notIn the vicinity of any given point, a In the vicinity of any given point, a gravitational field is equivalent to an gravitational field is equivalent to an accelerated frame of reference without a accelerated frame of reference without a gravitational fieldgravitational field

This is the This is the principle of equivalenceprinciple of equivalence

Implications of General Implications of General RelativityRelativity

Gravitational mass and inertial mass are not just Gravitational mass and inertial mass are not just proportional, but completely equivalentproportional, but completely equivalentA clock in the presence of gravity runs more A clock in the presence of gravity runs more slowly than one where gravity is negligibleslowly than one where gravity is negligibleThe frequencies of radiation emitted by atoms in The frequencies of radiation emitted by atoms in a strong gravitational field are shifted to lower a strong gravitational field are shifted to lower frequenciesfrequencies

This has been detected in the spectral lines emitted This has been detected in the spectral lines emitted by atoms in massive starsby atoms in massive stars

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QUICK QUIZ 26.5

Two identical clocks are in the same house, one Two identical clocks are in the same house, one upstairs in a bedroom and the other downstairs in upstairs in a bedroom and the other downstairs in the kitchen. Which statement is correct? (a) The the kitchen. Which statement is correct? (a) The clock in the kitchen runs more slowly than the clock in the kitchen runs more slowly than the

clock in the bedroom. (b) The clock in the clock in the bedroom. (b) The clock in the bedroom runs more slowly than the clock in the bedroom runs more slowly than the clock in the

kitchen. (c) Both clocks keep the same time.kitchen. (c) Both clocks keep the same time.

QUICK QUIZ 26.5 ANSWER

(a). The downstairs clock runs more (a). The downstairs clock runs more slowly because it is closer to the Earth slowly because it is closer to the Earth and hence experiences a stronger and hence experiences a stronger gravitational field than the upstairs clock gravitational field than the upstairs clock does.does.

The time difference between the two clocks is about 4x10-16 s for each second that passes on the clock.Too small to observe without expensive equipment!

More Implications of General More Implications of General RelativityRelativity

A gravitational field may be A gravitational field may be ““transformed transformed awayaway”” at any point if we choose an at any point if we choose an appropriate accelerated frame of reference appropriate accelerated frame of reference –– a freely falling framea freely falling frameEinstein specified a certain quantity, the Einstein specified a certain quantity, the curvature of timecurvature of time--spacespace, that describes the , that describes the gravitational effect at every pointgravitational effect at every point

Curvature of SpaceCurvature of Space--TimeTime

There is no such thing as a gravitational There is no such thing as a gravitational fieldfield

According to EinsteinAccording to EinsteinInstead, the presence of a mass causes a Instead, the presence of a mass causes a curvature of timecurvature of time--space in the vicinity of space in the vicinity of the massthe mass

This curvature dictates the path that all freely This curvature dictates the path that all freely moving objects must followmoving objects must follow

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Testing General RelativityTesting General Relativity

General Relativity predicts that a light ray passing near General Relativity predicts that a light ray passing near the Sun should be deflected by the curved spacethe Sun should be deflected by the curved space--time time created by the Suncreated by the Sun’’s masss massThe prediction was confirmed by astronomers during a The prediction was confirmed by astronomers during a total solar eclipsetotal solar eclipse

Black HolesBlack Holes

If the concentration of mass becomes If the concentration of mass becomes great enough, a black hole is believed to great enough, a black hole is believed to be formedbe formedIn a black hole, the curvature of spaceIn a black hole, the curvature of space--time is so great that, within a certain time is so great that, within a certain distance from its center, all light and distance from its center, all light and matter become trappedmatter become trapped

Quantum PhysicsQuantum Physics

Chapter 27Chapter 27Objectives27.1 Explain how blackbody radiation implies the quantization of electromagnetic energy. 27.2 Describe how Einstein's photoelectric equation implies the existence of the photon. 27.3 Define bremsstrahlung radiation. 27.4 Explain how X-ray diffraction can be used to determine crystal structure. 27.5 Solve sample problems that demonstrate the particle-like aspects of radiation as predicted by the Compton effect. 27.6 Identify the particle and wave-like aspects of electromagnetic radiation. 27.7 Identify the wave-like aspects of particles, citing examples. 27.8 Define the wave function for particles. 27.9 Summarize the key aspects of the uncertainty principle. 27.10 Describe the operation of the scanning tunneling microscope.

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Need for Quantum PhysicsNeed for Quantum PhysicsProblems remained from classical mechanics Problems remained from classical mechanics that relativity didnthat relativity didn’’t explaint explainBlackbody RadiationBlackbody Radiation

The electromagnetic radiation emitted by a heated The electromagnetic radiation emitted by a heated objectobject

Photoelectric EffectPhotoelectric EffectEmission of electrons by an illuminated metalEmission of electrons by an illuminated metal

Spectral LinesSpectral LinesEmission of sharp spectral lines by gas atoms in an Emission of sharp spectral lines by gas atoms in an electric discharge tubeelectric discharge tube

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Development of Quantum Development of Quantum PhysicsPhysics

1900 to 19301900 to 1930Development of ideas of quantum mechanicsDevelopment of ideas of quantum mechanics

Also called wave mechanicsAlso called wave mechanicsHighly successful in explaining the behavior of atoms, Highly successful in explaining the behavior of atoms, molecules, and nucleimolecules, and nuclei

Quantum Mechanics reduces to classical mechanics Quantum Mechanics reduces to classical mechanics when applied to macroscopic systemswhen applied to macroscopic systemsInvolved a large number of physicistsInvolved a large number of physicists

Planck introduced basic ideasPlanck introduced basic ideasMathematical developments and interpretations involved Mathematical developments and interpretations involved such people as such people as Einstein, Bohr, SchrEinstein, Bohr, Schröödinger, de Broglie, dinger, de Broglie, Heisenberg, Born and DiracHeisenberg, Born and Dirac

Blackbody RadiationBlackbody Radiation

An object at any temperature is An object at any temperature is known to emit electromagnetic known to emit electromagnetic radiationradiation

Sometimes called Sometimes called thermal radiationthermal radiationStefanStefan’’s Law describes the total power s Law describes the total power radiatedradiated

The spectrum of the radiation depends The spectrum of the radiation depends on the temperature and properties of on the temperature and properties of the objectthe object

4P AeTσ=emissivityStefan’s constant

Black Body RadiationBlack Body Radiation Blackbody Radiation GraphBlackbody Radiation GraphExperimental data for Experimental data for distribution of energy in distribution of energy in blackbody radiationblackbody radiationAs the temperature As the temperature increases, the total increases, the total amount of energy amount of energy increasesincreases

Shown by the area under Shown by the area under the curvethe curve

As the temperature As the temperature increases, the peak of the increases, the peak of the distribution shifts to distribution shifts to shorter wavelengthsshorter wavelengths

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WienWien’’s Displacement Laws Displacement LawThe wavelength of the peak of the blackbody The wavelength of the peak of the blackbody distribution was found to follow distribution was found to follow WeinWein’’s s Displacement Law Displacement Law

λλmaxmaxTT = 0.2898 x 10= 0.2898 x 10--22 m m •• KK

λλmaxmax is the wavelength at the curveis the wavelength at the curve’’s peaks peakT is the absolute temperature of the object emitting T is the absolute temperature of the object emitting the radiationthe radiation

The Ultraviolet CatastropheThe Ultraviolet CatastropheClassical theory did not Classical theory did not match the experimental match the experimental datadataAt long wavelengths, the At long wavelengths, the match is goodmatch is goodAt short wavelengths, At short wavelengths, classical theory predicted classical theory predicted infinite energyinfinite energyAt short wavelengths, At short wavelengths, experiment showed no experiment showed no energyenergyThis contradiction is called This contradiction is called the the ultraviolet catastropheultraviolet catastrophe

PlanckPlanck’’s Resolutions ResolutionPlanck hypothesized that the blackbody Planck hypothesized that the blackbody radiation was produced by radiation was produced by resonatorsresonators

Resonators were submicroscopic charged oscillatorsResonators were submicroscopic charged oscillatorsThe resonators could only have The resonators could only have discrete discrete energiesenergies

EEnn = n h = n h ƒƒn is called the n is called the quantum numberquantum numberƒƒ is the frequency of vibrationis the frequency of vibrationh is h is PlanckPlanck’’s constants constant, , 6.626 x 106.626 x 10--3434 J sJ s

Key point is quantized energy statesKey point is quantized energy states

Problem: a Problem: a lightbulblightbulb

Assuming that the tungsten filament of a Assuming that the tungsten filament of a lightbulblightbulb is a blackbody, is a blackbody, determine its peak wavelength if its temperature is 2 900 K.determine its peak wavelength if its temperature is 2 900 K.

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Assuming that the tungsten filament of a Assuming that the tungsten filament of a lightbulblightbulb is a blackbody, determine its is a blackbody, determine its peak wavelength if its temperature is 2 900 K.peak wavelength if its temperature is 2 900 K.

Given:

T = 2900 K2900 K

Find:

λmax = ?

Recall Wein;s law: λλmaxmax T = 0.2898 x 10T = 0.2898 x 10--22 m m •• K.K. It can be used to solve for λmax:

2

max0.2898 10 m K

Tλ

−× ⋅=

( )27

max

0.2898 109.99 10 999

2900

m Km nm

Kλ

−−

× ⋅= = × =

Thus,

This is infrared, so most of the electric energy goes into heat!

Photoelectric EffectPhotoelectric EffectWhen light is incident on certain metallic When light is incident on certain metallic surfaces, electrons are emitted from the surfacesurfaces, electrons are emitted from the surface

This is called the This is called the photoelectric effectphotoelectric effectThe emitted electrons are called The emitted electrons are called photoelectronsphotoelectrons

The effect was first discovered by HertzThe effect was first discovered by HertzThe successful explanation of the effect was The successful explanation of the effect was given by Einstein in 1905given by Einstein in 1905

Received Nobel Prize in 1921 for paper on Received Nobel Prize in 1921 for paper on electromagnetic radiation, of which the photoelectric electromagnetic radiation, of which the photoelectric effect was a parteffect was a part

Photoelectric Effect SchematicPhotoelectric Effect SchematicWhen light strikes E, When light strikes E, photoelectrons are photoelectrons are emittedemittedElectrons collected at C Electrons collected at C and passing through the and passing through the ammeter are a current in ammeter are a current in the circuitthe circuitC is maintained at a C is maintained at a positive potential by the positive potential by the power supplypower supply

Photoelectric Current/Voltage Photoelectric Current/Voltage GraphGraph

The current increases The current increases with intensity, but with intensity, but reaches a saturation level reaches a saturation level for large for large ΔΔVV’’ssNo current flows for No current flows for voltages less than or voltages less than or equal to equal to ––ΔΔVVss, the , the stopping potentialstopping potential

The stopping potential is The stopping potential is independent of the independent of the radiation intensityradiation intensity

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Features Not Explained by Classical Features Not Explained by Classical Physics/Wave TheoryPhysics/Wave Theory

No electrons are emitted if the incident light frequency is No electrons are emitted if the incident light frequency is below some below some cutoff frequencycutoff frequency that is characteristic of the that is characteristic of the material being illuminatedmaterial being illuminatedThe maximum kinetic energy of the photoelectrons is The maximum kinetic energy of the photoelectrons is independent of the light intensityindependent of the light intensityThe maximum kinetic energy of the photoelectrons The maximum kinetic energy of the photoelectrons increases with increasing light frequencyincreases with increasing light frequencyElectrons are emitted from the surface almost Electrons are emitted from the surface almost instantaneously, even at low intensitiesinstantaneously, even at low intensities

EinsteinEinstein’’s Explanations Explanation

A tiny packet of light energy, called a A tiny packet of light energy, called a photonphoton, would be emitted , would be emitted when a quantized oscillator jumped from one energy level to the when a quantized oscillator jumped from one energy level to the next lower onenext lower one

Extended PlanckExtended Planck’’s idea of quantization to electromagnetic s idea of quantization to electromagnetic radiationradiation

The photonThe photon’’s energy would be s energy would be E = hE = hƒƒEach photon can give all its energy to an electron in the metalEach photon can give all its energy to an electron in the metalThe maximum kinetic energy of the liberated photoelectron is The maximum kinetic energy of the liberated photoelectron is

KE = hKE = hƒƒ –– ΦΦ

ΦΦ is called the is called the work functionwork function of the metalof the metal

Explanation of Classical Explanation of Classical ““ProblemsProblems””

The effect is not observed below a certain The effect is not observed below a certain cutoff frequency since the photon energy cutoff frequency since the photon energy must be greater than or equal to the work must be greater than or equal to the work functionfunction

Without this, electrons are not emitted, Without this, electrons are not emitted, regardless of the intensity of the lightregardless of the intensity of the light

The maximum KE depends only on the The maximum KE depends only on the frequency and the work function, not on frequency and the work function, not on the intensitythe intensity

More ExplanationsMore Explanations

The maximum KE increases with The maximum KE increases with increasing frequencyincreasing frequencyThe effect is instantaneous since there is a The effect is instantaneous since there is a oneone--toto--one interaction between the photon one interaction between the photon and the electronand the electron

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Verification of EinsteinVerification of Einstein’’s Theorys Theory

Experimental Experimental observations of a observations of a linear relationship linear relationship between KE and between KE and frequency confirm frequency confirm EinsteinEinstein’’s theorys theoryThe xThe x--intercept is the intercept is the cutoff frequencycutoff frequency

cf hΦ

=

Problem: photoelectric effectProblem: photoelectric effect

Electrons are ejected from a metallic surface with speeds ranginElectrons are ejected from a metallic surface with speeds ranging g up to 4.6 up to 4.6 ×× 101055 m/sm/s when light with a wavelength of when light with a wavelength of λλ = 625 nm = 625 nm is used. is used. (a) What is the work function of the surface? (a) What is the work function of the surface? (b) What is the cutoff frequency for this surface?(b) What is the cutoff frequency for this surface?

Electrons are ejected from a metallic surface with speeds ranginElectrons are ejected from a metallic surface with speeds ranging up to 4.6 g up to 4.6 ×× 101055 m/sm/swhen light with a wavelength of when light with a wavelength of λλ = 625 nm is used. = 625 nm is used. (a) What is the work function of the surface? (a) What is the work function of the surface? (b) What is the cutoff frequency for this surface?(b) What is the cutoff frequency for this surface?

Given:

v = 4.6x105 m/sλ = 625 nm

Find:

φ = ?ν =?

Recall that KEKEmaxmax==hfhf -- φφ. This can be used to solve for φ. First find the kinetic energy

( )( )2

31 5 20maxmax

1 9.11 10 4.6 10 9.6 102 2

mvKE kg m s J− −= = × × = ×

Thus,

Cutoff frequency is

1914

34

2.2 10 3.3 106.63 10c

Jf Hzh J s

−

−

Φ ×= = = ×

× ⋅

19max max 2.2 10hchf KE KE J

λ−Φ = − = − = ×

Which equals 1.4 eV

PhotocellsPhotocells

Photocells are an application of the Photocells are an application of the photoelectric effectphotoelectric effectWhen light of sufficiently high frequency When light of sufficiently high frequency falls on the cell, a current is producedfalls on the cell, a current is producedExamplesExamples

Streetlights, garage door openers, elevatorsStreetlights, garage door openers, elevators

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XX--RaysRays

Electromagnetic radiation with short Electromagnetic radiation with short wavelengthswavelengths

Wavelengths less than for ultravioletWavelengths less than for ultravioletWavelengths are typically about 0.1 nmWavelengths are typically about 0.1 nmXX--rays have the ability to penetrate most rays have the ability to penetrate most materials with relative easematerials with relative ease

Discovered and named by Roentgen in Discovered and named by Roentgen in 18951895

Production of XProduction of X--rays, 1rays, 1XX--rays are produced when rays are produced when highhigh--speed electrons are speed electrons are suddenly slowed downsuddenly slowed down

Can be caused by the electron Can be caused by the electron striking a metal targetstriking a metal target

A current in the filament A current in the filament causes electrons to be causes electrons to be emittedemittedThese freed electrons are These freed electrons are accelerated toward a dense accelerated toward a dense metal targetmetal targetThe target is held at a higher The target is held at a higher potential than the filamentpotential than the filament

Production of XProduction of X--rays, 2rays, 2An electron passes near An electron passes near a target nucleusa target nucleusThe electron is deflected The electron is deflected from its path by its from its path by its attraction to the nucleusattraction to the nucleus

This produces an This produces an accelerationacceleration

It will emit It will emit electromagnetic radiation electromagnetic radiation when it is acceleratedwhen it is accelerated

Diffraction of XDiffraction of X--rays by Crystalsrays by Crystals

For diffraction to occur, the spacing For diffraction to occur, the spacing between the lines must be approximately between the lines must be approximately equal to the wavelength of the radiation to equal to the wavelength of the radiation to be measuredbe measuredFor XFor X--rays, the regular array of atoms in a rays, the regular array of atoms in a crystal can act as a threecrystal can act as a three--dimensional dimensional grating for diffracting Xgrating for diffracting X--raysrays

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Schematic for XSchematic for X--ray Diffractionray DiffractionA continuous beam of XA continuous beam of X--rays is incident on the rays is incident on the crystalcrystalThe diffracted radiation is The diffracted radiation is very intense in certain very intense in certain directionsdirections

These directions correspond These directions correspond to constructive interference to constructive interference from waves reflected from the from waves reflected from the layers of the crystallayers of the crystal

The diffraction pattern is The diffraction pattern is detected by photographic detected by photographic filmfilm

Photo of XPhoto of X--ray Diffraction ray Diffraction PatternPattern

The array of spots is called The array of spots is called a a LaueLaue patternpatternThe crystal structure is The crystal structure is determined by analyzing the determined by analyzing the positions and intensities of positions and intensities of the various spotsthe various spotsThis is for NaClThis is for NaCl

BraggBragg’’s Laws LawThe beam reflected from the The beam reflected from the lower surface travels farther lower surface travels farther than the one reflected from than the one reflected from the upper surfacethe upper surfaceIf the path difference equals If the path difference equals some integral multiple of the some integral multiple of the wavelength, constructive wavelength, constructive interference occursinterference occursBraggBragg’’s Laws Law gives the gives the conditions for constructive conditions for constructive interferenceinterference

2 d sin 2 d sin θθ = m = m λλ, m = 1, 2, 3, m = 1, 2, 3……

The Compton EffectThe Compton EffectCompton directed a beam of xCompton directed a beam of x--rays toward a rays toward a block of graphiteblock of graphiteHe found that the scattered xHe found that the scattered x--rays had a slightly rays had a slightly longer wavelength that the incident xlonger wavelength that the incident x--raysrays

This means they also had less energyThis means they also had less energyThe amount of energy reduction depended on The amount of energy reduction depended on the angle at which the xthe angle at which the x--rays were scatteredrays were scatteredThe change in wavelength is called the The change in wavelength is called the Compton Compton shiftshift

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Compton ScatteringCompton ScatteringCompton assumed the Compton assumed the photons acted like photons acted like other particles in other particles in collisionscollisionsEnergy and momentum Energy and momentum were conservedwere conservedThe shift in wavelength The shift in wavelength isis

(1 cos )oe

hm c

λ λ λ θΔ = − = −

Compton Scattering, finalCompton Scattering, final

The quantity h/mThe quantity h/meec is called the c is called the Compton Compton wavelengthwavelength

Compton wavelength = 0.00243 nmCompton wavelength = 0.00243 nmVery small compared to visible lightVery small compared to visible light

The Compton shift depends on the scattering The Compton shift depends on the scattering angle and not on the wavelengthangle and not on the wavelengthExperiments confirm the results of Compton Experiments confirm the results of Compton scattering and strongly support the photon scattering and strongly support the photon conceptconcept

QUICK QUIZ 27.1

An xAn x--ray photon is scattered by an ray photon is scattered by an electron. The frequency of the scattered electron. The frequency of the scattered

photon relative to that of the incident photon relative to that of the incident photon (a) increases, (b) decreases, or (c) photon (a) increases, (b) decreases, or (c)

remains the same.remains the same.

QUICK QUIZ 27.1 ANSWER

(b). Some energy is transferred to the (b). Some energy is transferred to the electron in the scattering process. electron in the scattering process.

Therefore, the scattered photon must Therefore, the scattered photon must have less energy (and hence, lower have less energy (and hence, lower frequency) than the incident photon.frequency) than the incident photon.

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QUICK QUIZ 27.2

A photon of energy A photon of energy EE00 strikes a free electron, strikes a free electron, with the scattered photon of energy with the scattered photon of energy EE moving moving in the direction opposite that of the incident in the direction opposite that of the incident photon. In this Compton effect interaction, photon. In this Compton effect interaction,

the resulting kinetic energy of the electron is the resulting kinetic energy of the electron is (a) (a) EE0 0 , (b) , (b) EE , (c) , (c) EE00 −− E ,E , (d) (d) EE0 0 + + E , E , (e) (e)

none of the above.none of the above.

QUICK QUIZ 27.2 ANSWER

(c). Conservation of energy requires (c). Conservation of energy requires the kinetic energy given to the electron the kinetic energy given to the electron be equal to the difference between the be equal to the difference between the energy of the incident photon and that energy of the incident photon and that

of the scattered photon.of the scattered photon.

QUICK QUIZ 27.3

A photon of energy A photon of energy EE0 0 strikes a free electron strikes a free electron with the scattered photon of energy with the scattered photon of energy E E moving moving in the direction opposite that of the incident in the direction opposite that of the incident photon. In this Compton effect interaction, photon. In this Compton effect interaction, the resulting momentum of the electron is: the resulting momentum of the electron is:

(a) (a) EE00/c/c (b) < (b) < EE00/c/c(c) > (c) > EE00/c/c (d) ((d) (EE00 −− EE)/)/cc(e) ((e) (EE −− EEoo)/)/cc

photonE pc=

QUICK QUIZ 27.3 ANSWER

(c). Conservation of momentum requires the (c). Conservation of momentum requires the momentum of the incident photon equal the momentum of the incident photon equal the vector sum of the vector sum of the momentamomenta of the electron of the electron and the scattered photon. Since the scattered and the scattered photon. Since the scattered photon moves in the direction opposite that of photon moves in the direction opposite that of the electron, the magnitude of the electronthe electron, the magnitude of the electron’’s s momentum must exceed that of the incident momentum must exceed that of the incident photon.photon.

0electron

E Epc+

=