Nuclear Physics

1
Nuclear Physics
2
Quantum Physics

• Physics on a very small (e.g., atomic) scale is
  quantized.
• Quantized phenomena are discontinuous and
  discrete, and generally very small.
• Quantized energy can be thought of as existing in
  packets of energy of specific size.
• Atoms can absorb and emit quanta of energy, but
  the energy intervals are very tiny, and not all
  energy levels are allowed for a given atom.

3
Light Ray

• We know from geometric optics that light behaves
  as a ray. This means it travels in a straight
  line.
• When we study ray optics, we ignore the nature of
  light, and focus on how it behaves when it hits a
  boundary and reflects or refracts at that
  boundary.

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Light Wave

• We will frequently use one equation from wave
  optics in quantum optics.
• c ?f
• c 3 x 108m/s (the speed of light in a vacuum)
• ? wavelength (m) (distance from crest to crest)
• f frequency (Hz or s-1)

5
Light Particle

• Light has a dual nature. In addition to behaving
  as a wave, it also behaves like a particle.
• It has energy and momentum, just like particles
  do. Particle behavior is pronounced on a very
  small level, or at very high light energies.
• A particle of light is called a photon.

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Photon Energy

• The energy of a photon is calculated from it the
  frequency of the light.
• E hf
• E energy (J or eV)
• h Plancks constant
• 6.62510-34 J s
• 4.14 10-15 eV s
• f frequency of light (s-1, Hz)

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Check

• Which has more energy in its photons, a very
  bright, powerful red laser or a small key-ring
  red laser?
• Which has more energy in its photons, a red laser
  or a green laser?

8
Electron Volts

• The electron-volt is the most useful unit on the
  atomic level.
• If a moving electron is stopped by 1 V of
  electric potential, we say it has 1 electron-volt
  (or 1 eV) of kinetic energy.
• 1 eV 1.60210-19 J

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Problem

• What is the frequency and wavelength of a photon
  whose energy is 4.0 x 10-19 J?

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Problem

• How many photons are emitted per second by a
  He-Ne laser that emits 3.0 mW of power at a
  wavelength of 632.8 nm?

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Atomic Transitions
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Energy Levels

• This graph shows allowed quantized energy levels
  in a hypothetical atom.
• The more stable states are those in which the
  atom has lower energy.
• The more negative the state, the more stable the
  atom.

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Energy Levels

• The highest allowed energy is 0.0 eV. Above this
  level, the atom loses its electron. This level is
  called the ionization level.
• The lowest allowed energy is called the ground
  state. This is where the atom is most stable.
• States between the highest and lowest state are
  called excited states.

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Energy Levels

• Transitions of the electron within the atom must
  occur from one allowed energy level to another.
• The electron CANNOT EXIST between energy levels.

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Photon Absorption

• When a photon of light is absorbed by an atom, it
  causes an increase in the energy of the atom.
• The photon disappears.
• The energy of the atom increases by exactly the
  amount of energy contained in the photon.
• The photon can be absorbed ONLY if it can produce
  an allowed energy increase in the atom.

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Photon Absorption

• When a photon is absorbed, it excites the atom to
  higher quantum energy state.
• The increase in energy of the atom is given by ?E
  hf.

0eV
-10eV
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Absorption Spectra

• When an atom absorbs photons, it removes the
  photons from the white light striking the atom,
  resulting in dark bands in the spectrum.
• Therefore, a spectrum with dark bands in it is
  called an absorption spectrum.

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Absorption Spectra

• Absorption spectra always involve atoms going up
  in energy level.

0eV
-10eV
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Photon Emission

• When a photon of light is emitted by an atom, it
  causes a decrease in the energy of the atom.
• A photon of light is created.
• The energy of the atom decreases by exactly the
  amount of energy contained in the photon that is
  emitted.
• The photon can be emitted ONLY if it can produce
  an allowed energy decrease in an excited atom.

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Photon Emission

• When a photon is emitted from an atom, the atom
  drops to lower quantum energy state.
• The drop in energy can be computed by ?E hf.

0eV
-10eV
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Emission Spectra

• When an atom emits photons, it glows! The photons
  cause bright lines of light in a spectrum.
• Therefore, a spectrum with bright bands in it is
  called an emission spectrum.

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Emission Spectra

• Emission spectra always involve atoms going down
  in energy level.

0eV
-10eV
23
Problem

• What is the frequency and wavelength of the light
  that will cause the atom shown to transition from
  the ground state to the first excited state? Draw
  the transition.

24
Problem

• What is the longest wavelength of light that when
  absorbed will cause the atom shown to ionize from
  the ground state? Draw the transition.

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Problem

• The atom shown is in the second excited state.
  What frequencies of light are seen in its
  emission spectrum? Draw the transitions.

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The Photoelectric Effect
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Absorption

• Weve seen that if you shine light on atoms, they
  can absorb photons and increase in energy.
• The transition shown is the absorption of an 8.0
  eV photon by this atom.
• You can use Plancks equation to calculate the
  frequency and wavelength of this photon.

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Extra Energy

• Now, suppose a photon with TOO MUCH ENERGY
  encounters an atom?
• If the atom is photo-active, a very interesting
  and useful phenomenon can occur
• This is called the Photoelectric Effect.

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Photoelectric Effect

• Some photoactive metals can absorb photons that
  not only ionize the metal, but give the electron
  enough kinetic energy to escape from the atom and
  travel away from it.
• The electrons that escape are often called
  photoelectrons.
• The binding energy or work function is the
  energy necessary to promote the electron to the
  ionization level.
• The kinetic energy of the electron is the extra
  energy provided by the photon.

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Photoelectric Effect

• Photon Energy Work Function Kinetic Energy
• hf ? Kmax
• Kmax hf ?
• Kmax Kinetic energy of photoelectrons
• hf energy of the photon
• ? binding energy or work function of the
  metal.

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Problem

• Suppose the maximum wavelength a photon can have
  and still eject an electron from a metal is 340
  nm. What is the work function of the metal
  surface?

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Photoelectric Effect

• Suppose you collect Kmax and frequency data for a
  metal at several different frequencies. You then
  graph Kmax for photoelectrons on y-axis and
  frequency on x-axis. What information can you get
  from the slope and intercept of your data?

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The Photoelectric Effect

• The Photoelectric Effect experiment is one of the
  most famous experiments in modern physics.
• The experiment is based on measuring the
  frequencies of light shining on a metal (which is
  controlled by the scientist), and measuring the
  resulting energy of the photoelectrons produced
  by seeing how much voltage is needed to stop
  them.
• Albert Einstein won the Nobel Prize by explaining
  the results.

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Photoelectric Effect Diagram
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Photoelectric Effect

• Voltage necessary to stop electrons is
  independent of intensity (brightness) of light.
  It depends only on the lights frequency (or
  color).
• Photoelectrons are not released below a certain
  frequency, regardless of intensity of light.
• The release of photoelectrons is instantaneous,
  even in very feeble light, provided the frequency
  is above the cutoff.

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Photoelectric Effect

• The kinetic energy of photoelectrons can be
  determined from the voltage (stopping potential)
  necessary to stop the electron.
• If it takes 6.5 Volts to stop the electron, it
  has 6.5 eV of kinetic energy.

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Momentum
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Mass of a Photon

• Photons do not have rest mass. They must travel
  at the speed of light, and nothing can travel at
  the speed of light unless its mass is zero.
• A photon has a fixed amount of energy (E hf).
• We can calculate how much mass would have to be
  destroyed to create a photon (Emc2).

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Problem

• Calculate the mass that must be destroyed to
  create a photon of 340nm light.

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Photon Momenum

• Photons do not have rest mass, yet they have
  momentum! This momentum is evident in that, given
  a large number of photons, they create a
  pressure.
• A photons momentum is calculated by

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Proof of Photon Momentum

• Compton scattering
• Proof that photons have momentum.
• High-energy photons collided with electrons
  exhibit conservation of momentum.
• Work Compton problems just like other
  conservation of momentum problems
• except the momentum of a photon uses a different
  equation.

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Problem

• What is the momentum of photons that have a
  wavelength of 620 nm?

43
Problem

• What is the frequency of a photon that has the
  same momentum as an electron with speed 1200 m/s?

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Matter Waves
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Matter Waves

• Waves act like particles sometimes and particles
  act like waves sometimes.
• This is most easily observed for very energetic
  photons (gamma or x-Ray) or very tiny particles
  (elections or nucleons)

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Energy

• A moving particle has kinetic energy
• E K ½ mv2
• A particle has most of its energy locked up in
  its mass.
• E mc2
• A photons energy is calculated using its
  frequency
• E hf

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Momentum

• For a particle that is moving
• p mv
• For a photon
• p h/?
• Units?

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Wavelength

• For a photon
• ? c/f
• For a particle, which has an actual mass, this
  equation still works
• ? h/p where p mv
• This is referred to as the deBroglie wavelength

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Matter Wave Proof

• Davisson-Germer Experiment
• Verified that electrons have wave properties by
  proving that they diffract.
• Electrons were shone on a nickel surface and
  acted like light by diffraction and interference.

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Problem

• What is the wavelength of a 2,200 kg elephant
  running at 1.2 m/s?

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Nuclear Decay
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Notation
Atomic Mass (Protons Neutrons)
Element
Atomic Number (Protons)
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Isotopes

• Isotopes have the same atomic number and
  different atomic mass.
• Isotopes have similar or identical chemistry.
• Isotopes have different nuclear behavior.

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Half Life

• The time required for one-half of an elements to
  decay.

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Nuclear Particles

• Proton
• Charge e
• Mass 1.66 x 10-27 kg (1 amu)
• Neutron
• Charge 0
• Mass 1.66 x 10-27 kg (1 amu)
• Electron
• Charge -e
• Mass 9.1 x 10-31 kg (1/2000 amu)

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Decay

• Nuclear Decay a spontaneous process in which an
  unstable nucleus ejects a particle and changes to
  another nucleus.
• Alpha decay
• Beta decay
• Beta Minus
• Positron
• Fission a nucleus splits into two fragments of
  roughly equal size.
• Fusion Two nuclei combine to form another
  nucleus.

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Decay

• Alpha decay
• A nucleus ejects an alpha particle, which is just
  a helium nucleus.
• Beta decay
• A nucleus ejects a negative electron.
• Positron decay
• A nucleus ejects a positive electron.

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Alpha Decay

• Alpha particle (helium nucleus) is released.
• Alpha decay only occurs with very heavy elements.

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Beta Decay

• Beta decay occurs when a nucleus has too many
  neutrons for the protons present.
• A neutron converts to a proton. An antineutrino
  is also released.

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Neutrinos

• Proposed to make beta and positron decay obey
  conservation of energy.
• These particles possess energy and spin, but do
  not possess mass or charge.
• They do not react easily with matter and are
  extremely hard to detect.

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Gamma Radiation

• Gamma photons are released by atoms which have
  just undergone a nuclear reaction when the
  excited new nucleus drops to its ground state.
• The high energy in a gamma photon is calculated
  by E hf.

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Energy in Nuclear Reaction
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Mass Energy

• Matter is created from energy and can be
  converted into energy through nuclear reactions.
• E mc2
• E Energy (J)
• M mass (kg)
• c speed of light (3x108m/s)

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Energy in Nuclear Reactions

1. Add up the mass (in atomic mass units, u) of the
   reactants.
2. Add up the mass (in atomic mass units, u) of the
   products.
3. Find the difference between reactant and product
   mass. The missing mass has been converted to
   energy.
4. Convert mass to kg ( 1 u 1.66 x 10-27 kg)
5. Use E mc2 to calculate energy released.

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Problem

• Complete the reaction, identify the type of
  decay, and calculate the energy.

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Fission

• Fission occurs when an unstable heavy nucleus
  splits apart into two lighter nuclei, forming two
  new elements.
• Fission can be induced by free neutrons.
• Mass is destroyed and energy produced according
  to E mc2.

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Fusion

• Fusion occurs when two light nuclei come together
  to form a new nucleus of a new element.
• Fusion is the most energetic of all nuclear
  reactions.
• Energy is produced by fusion in the sun.
• Fusion of light elements can result in
  non-radioactive waste.