Physics 2D Lecture Slides Lecture 12: Jan 26th 2005 · Classical Physics: Time Lag in...

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Transcript of Physics 2D Lecture Slides Lecture 12: Jan 26th 2005 · Classical Physics: Time Lag in...

  • 1

    Physics 2D Lecture SlidesLecture 12: Jan 26th 2005

    Vivek SharmaUCSD Physics

    Ultra Violet (Frequency) Catastrophe

    4 4

    Radianc

    c c 8 2 Radiancy

    y is Radiatio

    R( ) = u( ) = kT

    n intensity per

    u

    k

    nit interval

    T 4 4

    c! !" "

    "

    "

    "=

  • 2

    Disaster # 2 : Photo-Electric Effect

    Can tune Intensity, freq,

    i

    Light of intensity I, wavelength and frequency incident on a photo-cathode

    Measure characteristics of current in the circuit as a fn of I, f,

    Photo Electric Effect: Measurable Properties Rate of electron emission from cathode

    From current i seen in ammeter

    Maximum kinetic energy of emitted electron By applying retarding potential on electron moving towards Collector

    plate

    KMAX = eVS (VS = Stopping voltage)Stopping voltage no current flows

    Effect of different types of photo-cathode metal Time between shining light and first sign of photo-

    current in the circuit

  • 3

    Observation: Photo-Current Vs Frequency of Incident Light

    -VS

    I3 = 3I1

    I2 = 2I1

    I1= intensity

    f

    Stopping voltage VS is a measure of the Max kinetic energy of the electron

    Stopping Voltage Vs For Different Photocathode Surfaces

    eVS = KMAX = max KE

  • 4

    Retarding Potential Vs Light Frequency (f)Shining Light With Constant Intensity But different frequenciesLarger the frequency of light, larger is the stopping voltage (and

    thus the kinetic energy of the photoelectrons )

    f1 > f2 >f3

    f1f2

    f3

    Current i in circuit

    I

    Conclusions from the Experimental Observation

    Max Kinetic energy KMAX independent of Intensity I forlight of same frequency

    No photoelectric effect occurs if light frequency f isbelow a threshold no matter how high the intensity oflight

    For a particular metal, light with f > f0 causesphotoelectric effect IRRESPECTIVE of light intensity. f0 is characteristic of that metal

    Photoelectric effect is instantaneous !...not time delay

    Can one Explain all this Classically !

  • 5

    As light Intensity increased field amplitude larger E field and electrical force seen by the charged subatomic oscillators Larger

    More force acting on the subatomic charged oscillator More energy transferred to it Charged particle hooked to the atom should leave the surface with

    more Kinetic Energy KE !! The intensity of light shining rules !

    As long as light is intense enough , light of ANY frequency f shouldcause photoelectric effect

    Because the Energy in a Wave is uniformly distributed over theSpherical wavefront incident on cathode, thould be a noticeable timelag T between time is incident & the time a photo-electron isejected : Energy absorption time How much time ? Lets calculate it classically.

    Classical Explanation of Photo Electric EffectE

    !

    F eE=

    ! !

    Classical Physics: Time Lag in Photo-Electric Effect Electron absorbs energy incident on a surface area where the electron is confined

    size of atom in cathode metal Electron is bound by attractive Coulomb force in the atom, so it must absorb a

    minimum amount of radiation before its stripped off Example : Laser light Intensity I = 120W/m2 on Na metal

    Binding energy = 2.3 eV= Work Function Electron confined in Na atom, size 0.1nm ..how long before ejection ? Average Power Delivered PAV = I . A, A= r2 3.1 x 10-20 m2

    If all energy absorbed then E = PAV . T T = E / PAV

    Classical Physics predicts Measurable delay even by the primitive clocks of 1900

    But in experiment, the effect was observed to be instantaneous !!

    Classical Physics fails in explaining all results

    19

    2 20 2

    (2.3 )(1.6 10 / )0.10

    (120 / )(3.1 10 )

    eV J eVT S

    W m m

    !

    !

    "# = =

    "

  • 6

    Thats Disaster # 2 !

    Max Planck & Birth of Quantum Physics

    Planck noted the UltraViolet Catastrophe at high frequencyCooked calculation with new ideas so as bring:

    R() 0 as 0 f

    Back to Blackbody Radiation Discrepancy

    Cavity radiation as equilibrium exchange of energy between EM radiation & atomic oscillators present on walls of cavity Oscillators can have any frequency f But the Energy exchange between radiation and oscillator NOT continuous and arbitararyit is discrete in packets of same amount E = n hf , with n = 1,2 3.

    h = constant he invented, a very small number he made up

  • 7

    Plancks Charged Oscillators in a Black Body Cavity Planck did not know about electrons, Nucleus etc: They were not known

    Planck, Quantization of Energy & BB Radiation

    Keep the rule of counting how many waves fit in a BB Volume Radiation Energy in cavity is quantized EM standing waves of frequency f have energy

    E = n hf ( n = 1,2 ,3 10 .1000) Probability Distribution: At an equilibrium temp T, possible Energy of wave is distributed over a spectrum of states: P(E) = e(-E/kT) Modes of Oscillation with :

    Less energy E=hf = favored More energy E=hf = disfavored

    hf

    P(E)

    E

    e(-E/kT)

    By this statistics, large energy, high f modes of EM disfavored

  • 8

    Plancks Calculation

    2x

    2

    4

    3

    8( )

    4

    Odd looking form

    hcWhen large small

    kT

    1

    1

    11 ( ....]

    Recall e 1

    1 1

    ....2!

    2

    =

    3!

    hc

    kT

    hc

    kT

    hc

    e

    hc hce

    kT kT

    h

    x

    c

    c

    x

    R

    x

    !

    !

    "

    !

    !

    !

    !

    ! !

    !

    !

    +

    # $# $= % &% &' ('

    ) *# $+ ,% &+ ,% &

    -' (. /

    # $- =

    (

    0 1 0

    = + +

    + + + -1

    +

    % &' (

    4

    8

    plugging this in R( ) eq:

    ) (4

    cR

    kT

    hc

    kT!

    !

    !"!

    # $# $= % &% &' (' (

    Graph & CompareWith BBQ data

    Plancks Formula and Small

    4

    When is small (large f)

    1 1

    1

    Substituting in R( ) eqn:

    Just as seen in the experiment

    As 0,

    8( )

    4

    ( ) 0

    al dat

    0

    a

    hc

    kT

    h

    hc hc

    kT kT

    c

    k

    c

    kT

    T

    hc

    R e

    R

    e

    e

    e e! !

    !

    !

    !

    "!!

    !

    !

    !

    !

    #

    #

    #

    $ %$ %= & '& '( )( )

    *

    * *

    + =#

    ,

  • 9

    Plancks Explanation of BB Radiation

    Fit formula to Exptal data h = 6.56 x 10-34 J.S h = very very small

    Major Consequence of Plancks Formula

  • 10

    Resolving Disaster #2: Who You Gonna Call ?Amongst his lesser known talents was his ability to communicate.

    here he is greeting old friend: Conrad Habicht

    What are you up to? you frozen whale, you smoked, dried, canned piece of soul

    Clearly , like the electron, the phrase

    Whaddup Dog !

    had not been discovered by then !

    Einsteins Explanation of PhotoElectric Effect

    Light as bullets of photonsEnergy concentrated in photonsEnergy exchanged instantly Energy of EM Wave E= hf

    What Maxwell Saw of EM Waves What Einstein Saw of EM Waves

  • 11

    Einsteins Explanation of Photoelectric Effect Energy associated with EM waves in not uniformly distributed

    over wave-front, rather is contained in packets of stuffPHOTON

    E= hf = hc/ [ but is it the same h as in Plancks th.?] Light shining on metal emitter/cathode is a stream of photons of

    energy which depends on frequency f Photons knock off electron from metal instantaneously

    Transfer all energy to electron Energy gets used up to pay for Work Function (Binding Energy)

    Rest of the energy shows up as KE of electron KE = hf-

    Cutoff Frequency hf0 = (pops an electron, KE = 0) Larger intensity I more photons incident Low frequency light f not energetic enough to overcome work

    function of electron in atom

    Photo Electric & Einstein (Nobel Prize 1915)

    -VS

    I3 = 3I1 I2 = 2I1

    I1= intensity

    Light shining on metal cathode is made of photonsEnergy E, depends on frequency f , E = hf = h (c/)This QUANTUM of energy is used to knock off electron

    electro

    s

    n

    e

    E hf K

    V KE

    E

    hf

    !

    != =

    = +

    "

    =

  • 12

    Photo Electric & Einstein (Nobel Prize 1915)Light shining on metal cathode is made of photonsQuantum of Energy E = hf = KE + KE = hf -

    Shining Light With Constant Intensity

    f1 > f2 >f3

    f1f2

    f3

    Modern View of Photoelectric Effect

  • 13

    Is h same in Photoelectric Effect as BB Radiation?

    Slope h = 6.626 x 10-34 JSEinstein Nobel Prize!

    No matter where you travel in the galaxy and beyond..no matter what experimentYou do

    h : Plancks constant is same

    NOBEL PRIZE FOR PLANCK

    Work Function (Binding Energy) In Metals

  • 14

    2 2

    Light of Intensity I = 1.0 W/cm inc

    A

    Photoelectric Effect on An Iron Surfa

    ssume Fe reflects 96% of ligh

    ce:

    further on

    ident on

    ly 3% of

    1.0cm surfa

    incident li

    ce of

    ght i i

    F

    t

    e

    s V

    2(a) Intensity available for Ph. El eff I =3

    olet region ( = 250nm)

    barely above thres

    ect

    (b) how m

    hold frequency for Ph

    any photo-electrons e

    . El effec

    mitted per

    t

    #

    s

    % 4% (1.0 W/c

    econd ?

    m )

    of

    !

    " "

    8

    9

    34

    2

    9

    Power =

    h f hc

    (250 10 )(1.2 10 / ) =

    (6.6 10 )(3.0 1

    p3% 4

    0 / )

    hoto

    % (1.0 W/celectro

    mn

    )s

    m J s

    J s m s

    !

    # #

    #

    =

    " "

    " "

    " "i

    10

    -15

    9

    15 1

    -19

    0

    9

    =

    (c) Current in Ammeter : i = (1.6 10 )(1.5 10 )

    (d) Work Function = ( )( )

    2.4

    10

    h 4.14 1

    1.5 10

    f 1.1 10

    0

    =

    4.5 eV

    C A

    seV s

    #

    #

    " " =

    $ =

    "

    "

    " "i

    Facts

    The human eye is a sensitive photon detector at visiblewavelenghts: Need >5 photons of 550nm to register onyour optical sensor

    The Photographic process : Energy to Dissociate an AgBr molecule = 0.6eV

    Photosynthesis Process : 9 sunlight photon per reactioncycle of converting CO2 and water to carbohydrate & O2 chlorophyll absorbs best at 650-700 nm

    Designing Space Shuttle skin : Why Platinum is a goodthing

    designing Solar cells : picking your metal cathode

  • 15

    Photon & Relativity: Wave or a Particle ? Photon associated with EM waves, travel with speed =c For light (m =0) : Relativity says E2 = (pc)2 + (mc2)2

    E = pc But Planck tells us : E = hf = h (c/) Put them together : hc / = pc

    p = h/ Momentum of the photon (light) is inversely proportional

    to But we associate with waves & p with particles

    .what is going on?? A new paradigm of conversation with the

    subatomic particles : Quantum Physics

    X Rays Bremsstrahlung: The Braking Radiation EM radiation, produced by bombarding a metal target with energetic electrons. Produced in general by ALL decelerating charged particles X rays : very short 60-100 pm (10-12m), large frequency f Very penetrating because very energetic E = hf !!

    Useful for probing structure of sub-atomic Particles (and your teeth)

  • 16

    X Ray Production Mechanism

    when electron passes near a positively charged target nucleus contained in target material, its deflected from its path because of its electrical attraction , experiences acceleration. Rules of E&M say that any charged particle will emit radiation when accelerated. This EM radiation appears as photons. Since photo carries energy and momentum, the electron must lose same amount. If all of electrons energy is lost in just one singlecollision then

    max min

    min

    = hf or

    hc hce V

    e V!

    !" = =

    "

    X Ray Spectrum in Molybdenum (Mo) Braking radiation predicted by Maxwells eqn decelerated charged particle will radiate

    continuously Spikes in the spectrum are characteristic of

    the nuclear structure of target material andvaries between materials

    Shown here are the and lines forMolybdenum (Mo)

    To measure the wavelength, diffractiongrating is too wide, need smaller slitsAn atomic crystal lattice as diffractiongrating (Bragg)

  • 17

    X rays are EM waves of low wavelength, high frequency(and energy) and demonstrate characteristic features of awave Interference Diffraction

    To probe into a structure you need a light source withwavelength much smaller than the features of the objectbeing probed Good Resolution

  • 18

    Compton Effect: what should Happen Classically? Plane wave [f,] incident on

    a surface with loosely boundelectrons interaction ofE field of EM wave withelectron: F = eE

    Electron oscillates withf = fincident

    Eventually radiatesspherical waves withfradiated= fincident At all scattering angles, f &

    must be zero

    Time delay while theelectron gets a tan : soaksin radiation

    Compton Scattering : Setup & Results

    ( ' ) (1 cos )

    Scattered ' larger than incident

    ! ! ! "

    !

    # = $ % $

  • 19

    Compton Scattering Observations

    Compton Scattering : Summary of Observations

    How does one explain this startling anisotropy?

    ' (1 cos ) !

    Not isotropy in distribution of

    scatte

    ( - )

    red radiati n

    o

    ! ! ! "# = $ %

  • 20

    Compton Effect : Quantum (Relativistic) Pool

    Compton Scattering: Quantum Picture

    2

    e

    e

    e

    E+m '

    p = p'cos +p cos

    0 p'sin -p sin

    Use these to e

    Energy Conservation:

    Momentum Conserv

    liminate

    electron deflection

    angle (n ot measured

    :

    )

    ec E E

    ! "

    ! "

    = +

    =

    e

    e

    e

    2 2 2 2 4

    2

    e

    2 2

    e

    e

    2

    p 2 'cos

    p cos 'cos

    p sin 'sin

    Square and add

    Eliminate p & using

    E &

    E ( ')

    '

    e e

    e

    e

    p c m c

    E E m

    p p

    p

    E

    p pp p

    c

    ! "

    !

    "

    "

    =

    = # +

    +

    =

    = +

    #

    =

    #

    $

  • 21

    ( ) 2 2

    2 22

    2 2

    22

    2 2 2

    2 2

    2

    2

    2

    ( ')

    ' 2 ' 2( ')

    ( ' ) (

    2 'cos ( )

    EFor light p=

    c

    ' ( ') 'cos

    E-E' 1 )(1 co

    '

    ' '2 co

    (1 cos )EE'

    s

    s

    )

    e

    e

    e

    e

    E E m c

    EE E E

    m c

    E E EE E

    mc

    p pp p

    E

    E

    E

    E

    Emc

    h

    E Ec

    c c

    cm m

    c

    c

    !

    !

    !

    ! " " !

    #

    =

    # $ + $ = $

    # = $ $ #

    $ + =

    +

    % &$ + +'

    $ + $

    $ = $

    (

    % &$ +) *

    ' (

    Compton Scattering: The Quantum Picture

    2

    e

    e

    e

    E+m '

    p = p'cos +p cos

    0 p'sin -p sin

    Use these to e

    Energy Conservation:

    Momentum Conserv

    liminate

    electron deflection

    angle (n ot measured

    :

    )

    ec E E

    ! "

    ! "

    = +

    =

    ( ' ) ( )(1 cos )e

    h

    m c! ! "# = #

    Rules of Quantum Pool between Photon and Electron

  • 22

    Checking for h in Compton ScatteringPlot scattered photon data, calculate slope and measure h

    1-cos

    ( ' ) ( )(1 cos )e

    h

    m c! ! "# = #

    Its the same value for h again !!

    Comp

    ton wa

    veleng

    th C

    =h/m e

    c

    Energy Quantization is aUNIVERSAL characteristic of energy transactions !

    Interference of Waves: A Reminder

    '

    maxTwo Identical waves travel along +x and interefere

    to give a resulting wave y ( , ). The resulting wave form depends on relative phase differen

    ( , ) sin( - )

    ce

    between 2 waves. Shown

    f

    i i i iy x t y

    t

    x

    x

    k t! "= +

    2 = 0r

    3o , , " # #$ Read Ch17-8 from Resnick

    etal held in Ereserve

  • 23

    An X-ray Tube from 20th Century

    The High Energy Accelerator of 1900s: produced energetic light : XRay , gave new optic to subatomic phenomena

    Xray

    e

  • 24

    Bragg Scattering: Probing Atoms With X-Rays

    Constructive Interference when net phase difference is 0, 2 etcThis implied path difference traveled by two waves must be integral multiple of wavelength : n=2dsin

    X-ray detector

    X-Ray Picture of a DNA Crystal

  • 25

    Proteins inside Rhinovirus reconstructed by x-ray diffraction