6. Atomic and Nuclear Physics

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6. Atomic and Nuclear Physics

• Chapter 6.4 Interactions of matter with energy

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The Photoelectric effect

• Heinrich Hertz first observed this photoelectric
  effect in 1887.
• This, too, was one of those handful of phenomena
  that Classical Physics could not explain.
• Hertz had observed that, under the right
  conditions, when light is shined on a metal,
  electrons are released.

The photoelectric effect consists on the
emission of electrons from a metallic surface by
absorption of light (electromagnetic radiation).
Photoelectrons
Photosurface
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The Photoelectric effect

• An apparatus to investigate the photoelectric
  effect was set by Millikan and it allowed him to
  determine the charge of the electron.

• When light falls on the surface, the electrons
  are removed from the metals atoms and move
  towards the positive cathode completing the
  circuit and thus creating a current.

http//phet.colorado.edu/simulations/sims.php?sim
Photoelectric_Effect
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The Photoelectric effect

• Whether the photoelectric effect occurs or not
  depends only on
• The nature of the photosurface

• The frequency of the radiation

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The Photoelectric effect

• When the intensity of the light source increases
  so does the current.
• ?Current and intensity are directly
  proportional
• A high current can be due to
• Electrons with high speed
• Large number of electrons being emitted
• To determine what exactly happens we need to be
  able to determine the energy of the emitted
  electrons.
• This is done by connecting a battery between the
  photosurface and the collecting plate.

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The Photoelectric effect

• When the battery supplies a p.d. the charge of
  the collecting plate will be negative.
• This means that the negatively charged electrons
  can be stopped if a sufficiently negative p.d. is
  applied to the electrodes.

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The Photoelectric effect

• The electrons leave the photosurface with a
  certain amount of kinetic energy EK.

• To stop the electrons we must supply a potential
  difference (called stopping voltage) so that
• eVs EK

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The Photoelectric effect

• The stopping voltage stays the same no matter
  what the intensity of the light source is.
• This means that
• The intensity of light affects the number of
  electrons emitted but not their energy
• The energy of the electrons depends on the nature
  of light the larger the frequency, the larger
  the energy of the emitted electrons and thus the
  larger the stopping voltage

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Critical of threshold frequency

• The two graphs represent the EK of the electrons
  versus frequency
• These graphs tell us that
• there is a minimum frequency fc, called critical
  or threshold frequency, such that no electrons
  are emitted.
• if the frequency of the light source is less than
  fc then the photoelectric effect does not occur
• the threshold frequency only depends on the
  nature of the photosurface

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The Photoelectric effect - Observations

1. The intensity of the incident light does not
   affect the energy of the emitted electrons (only
   their number)
2. The electron energy depends on the frequency of
   the incident light, and there is a certain
   minimum frequency below which no electrons are
   emitted.
3. Electrons are emitted with no time delay
   instantaneous effect.

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The Photoelectric effect
Problem According to Classical Physics, the
electron should be able to absorb the energy from
light waves and accumulate it until it is enough
to be emitted.
Solution Einstein suggested that light could be
considered particles of light, photons, packets
of energy and momentum or quanta. The energy of
such quantum is give by E h f where f is
the frequency of the e-m radiation h
6.63x10-34J (constant known as Planck constant)
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The Photoelectric effect

• When a photon hits a photosurface, an electron
  will absorb that energy.
• However, part of that energy will be used to pull
  the electron from the nucleus.
• That energy is called the work function and
  represented by ?.
• The remaining energy will be the kinetic energy
  of the free electron.
• So,
• Ek hf - ?

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The Photoelectric effect

• Recalling that
• EK eVs
• So,
• eVs hf ?
• that is

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The Photoelectric effect

• When a photon hits a photosurface, 3 things can
  happen
• The energy of the photon is not enough to remove
  the electron ? nothing happens
• The energy of the photon is just enough to remove
  the electron the photons energy equals the
  ionization energy ? the electron leaves the atom
  without any Ek
• The energy of the photon is larger than the
  ionization energy ? the electron leaves the atom
  with Ek

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Exercise

1. What is the work function for the photosurface
   (in joules)?
2. What is the energy of the green photoelectron?
3. What is the speed of the green photoelectron?
4. What is the energy of the blue photoelectron?
5. What is the speed of the blue photoelectron?

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Exercise

1. What is the work function for the photosurface
   (in joules)?
2. What is the energy of the green photoelectron?
3. What is the speed of the green photoelectron?
4. What is the energy of the blue photoelectron?
5. What is the speed of the blue photoelectron?

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Light wave or particle

• The photon has an energy given by E hf
• But if it is considered a particle it also
  carries momentum
• p m v
• According to Einstein
• E m c2 ? m E /c2
• So,
• p (E /c2) c ? p E / c
• p hf /c
• p h /?

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Light wave or particle

• Light can behave as a particle and the
  photoelectric effect is evidence for that fact.
• But if we do Youngs double slit experiment so
  that make photons of light go through the slits
  one at each time, the photon will produce an
  interference pattern.
• Somehow, even when light behaves like a particle
  it conserves its wave properties.
• So, we talk about wave-particle duality.

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De Bröglies wavelength

• In 1923, Louis de Bröglie suggested that if light
  can behave as a particle then particles could
  have a wave associated to them.

Louis de Broglie

• The wave-particle duality or duality of matter
  can be applied to matter and energy.
• All particles have a wave associated to them so
  that
• ? h / p
• Big particles have a wavelength so small that it
  cant be measured.
• But small particles, like electrons, would have a
  wavelength that is possible to be measured.

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The electron as a wave

• To prove that the electron behaves like a wave it
  must have wave properties, such diffraction. To
  make an electron diffract around an obstacle of
  size d, its wavelength ? must be comparable to or
  bigger that d.
• An electron of mass 9.1x10-31kg and speed of 105
  m/s will have a wavelength ? 7.2x10-9m.

• To have an obstacle with this size we must look
  at the structure of crystals. The typical
  distance between atoms in a crystal is of the
  order of 10-8m. When electrons are made to pass
  through crystals, they do diffract thus proving
  its wave nature.

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Davisson and Germer experiment

• In this experiment, electrons of kinetic energy
  54eV were directed at a surface ok nickel where a
  single crystal had been grown and were scattered
  by it.
• Using the Bragg formula and the known separation
  of the crystal atoms allowed the determination of
  the wavelength which has then seen to agree with
  the De Broglie formula.

Structural analysis by electron diffraction