A potential difference V is

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A potential difference V is maintained between
the metal target and the collector cup
Electrons ejected from C travel to A and G
detects the flow
i
Apply voltage V between A and C to slow the
ejected electrons down
When potential matches the initial KE of the
electrons, the flow stops (most energetic
electrons stopped)
Kmax e Vstop
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Photoelectric Effect

• Vstop does not depend on the intensity of the
  light source for a given frequency f
• gt classical physics would predict that if we
  increase the amplitude of the alternating
  electric field, then a larger kick would be given
  to the electron?
• gt if light is composed of photons, then the
  maximum energy that an electron can pick up is
  that of a single photon

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High intensity
Adjust V in negative sense until current vanishes
All electrons reach collector
Kmax e Vstop
Independent of intensity!
Low intensity
Measure Vstop as a function of frequency f
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Photoelectric Effect

• In each case, there is a minimum frequency f0 for
  the effect to occur
• cannot be explained classically

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Photoelectric Effect

• Classical theory
• oscillating e/m fields in the light cause
  electrons in the metal to oscillate
• average KE amplitude2 (electric
  field)2Intensity
• Quantum theory
• light composed of energy packets called photons
  Ehf gtan electron absorbs one photon and
  gains energy hf (this process is independent
  of the intensity)
• not expected classically! gt increase intensity
  or wait longer for electron to absorb enough
  energy

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Photoelectric Effect
Why do electrons stay in metals? Electrical force
lowers the potential energy

• Electron needs a minimum amount of energy ? to
  escape
• ? depends on the type of metal gt called the work
  function
• if an electron absorbs a photon, then (hf - ?) is
  the amount of energy left over for KE

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Photoelectric Effect

• Hence we need hf gt ? to just escape
• that is f gt ?/h f0
• Einstein Kmax (hf - ?) if no other
  e Vstop losses of energy are involved
• Vstop (h/e) f - (?/e)

Slope h/e is independent of the metal!
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• units volts is a unit of electrical
  potential
• eV (1.6x10-19) volts is a unit of energy
  called an electron volt (eV)
• eVstop h f - ? h( f - f0) Kmax

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Problem

• A satellite in Earth orbit maintains a panel of
  solar cells of area 2.60 m2 oriented
  perpendicular to the direction of the Suns rays.
  Solar energy arrives at the rate of 1.39 kW/m2
  (energy/area/time)
• (a) at what rate does Solar energy strike the
  panel?
• rateenergy/time 1.39(2.60) 3.61 kW
• (b) at what rate are Solar photons absorbed
  ? (?550nm)
• each photon carries Ehc/? (6.63x10-34)(3x
  108)/(550x10-9)3.61x10-19 J
• photons/time (3.61x103)/(3.61x10-19 ) 1022
  /sec

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Problem

• (c) how long would it take for a mole of
  photons to be absorbed?
• NA 6.02 x 1023
• time NA/(number photons/time) (6.02 x
  1023)/1022 60.2 sec

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Problem

• Light strikes a sodium surface and causes
  photoelectric emission. If Vstop 5.0 volts and
  the work function ? is 2.2 eV, what is the
  wavelength of the light?
• Ephoton hf hc/?
• Kmax Ephoton - ? hc/? - ? e Vstop
• ? (hc)/(e Vstop ? )
• h 6.63x10-34 J.s 6.63x10-34 /1.6x10-19
  eV.s 4.14 x10-15 eV.s
• ? (4.14 x10-15 eV.s)(3x108m/s)/5.0 eV2.2 eV
  170 nm

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Momentum

• 1916 Einstein extended the photon idea
• when light interacts with matter, not only energy
  but also linear momentum is transferred via
  photons
• momentum is also transferred in discrete amounts
  phf/c h/? photon momentum
• Ehf hc/? phf/c h/?
• gt E pc
• recall that E2p2c2 m2c4 gt m0 massless
• short wavelength photons have more energy and
  momentum!

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Compton Effect

• 1923 Compton performed an experiment which
  supported this idea
• directed a beam of x-rays of wavelength ? onto a
  carbon target
• x-rays are scattered in different directions

? has 2 peaks
? 71.1 pm (10-12 m)
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Compton Scattering

• Wavelength ? of scattered x-rays has two peaks
• these occur at ? and ? ??
• ?? gt0 is the Compton shift
• classical physics predicts ?? 0
• Quantum picture
• a single photon interacts with electrons in the
  target
• light behaves like a particle of energy
  Ehfhc/? and momentum ph/ ? gt a collision

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Compton Scattering

• Conservation of energy E E K
• gt E lt E gt f lt f gt ? gt ?
• X-ray momentum ph/? p h/?
• electron momentum pe ?mev

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Compton Scattering

• Conservation of energy E E K
• gt E lt E gt f lt f gt ? gt ?
• X-ray momentum ph/? p h/?
• electron momentum pe ?mev

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X-ray scattering

• Energy and momentum are conserved
• Momentum is a vector! Fdp/dt0 gt p constant