Nuclear Physics

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Chapter 29

• Nuclear Physics

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Nuclear Physics Sections 14
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Milestones in Nuclear Physics

• 1896 the birth of nuclear physics
• Becquerel discovered radioactivity in uranium
  compounds
• 1911 Rutherford, Geiger and Marsden performed
  scattering experiments
• Established the point mass nature of the nucleus
• Nuclear force was a new type of force
• 1919 Rutherford and coworkers first observed
  nuclear reactions
• Naturally occurring alpha particles bombarded
  nitrogen nuclei to produce oxygen

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Some Properties of Nuclei

• All nuclei are composed of protons and neutrons
• Exception is ordinary hydrogen
  with just a proton
• Atomic number, Z
• Number of protons in the nucleus
• Neutron number, N
• Number of neutrons in the nucleus
• Mass number, A
• Number of nucleons in the nucleus A Z N
• Nucleon is a generic term used to refer to either
  a proton or a neutron in the nucleus
• The mass number is not the same as the mass

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Symbolism

• Symbol
• X is the chemical symbol of the element
• Example
• Mass number A 27 nucleons
• Atomic number Z 13 protons
• Neutron number N 27 13 14 neutrons
• The Z may be omitted since the element can be
  used to determine Z

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More Properties

• The nuclei of all atoms of a particular element
  must contain the same number of protons
• They may contain varying numbers of neutrons
• Isotopes of an element have the same Z but
  differing N and A values
• Example
• See Appendix B An Abbreviated Table of Isotopes

Radioactive
Stable
Stable
Radioactive
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Charge and Mass

• The proton has a single positive charge, e
• e 1.60217733 x 10-19 C
• The electron has a single negative charge, e
• The neutron has no charge difficult to detect
• It is convenient to use unified mass units, u, to
  express masses
• 1 u 1.660559 x 10-27 kg
• Based on definition that mass of one atom of 12C
  is exactly 12 u
• Mass can also be expressed in MeV/c2
• From E m c2 ? 1 u 931.494 MeV/c2

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Summary of Charges Masses
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The Size of the Nucleus

• First investigated by Rutherford in scattering
  experiments
• He found an expression for how close an alpha
  particle moving toward the nucleus can come
  before being turned around by the Coulomb force
• The KE of the particle must be completely
  converted to PE

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Size of the Nucleus, cont

• d gives an upper limit for the size of the
  nucleus
• Rutherford determined that

• For gold, he found d 3.2 x 10-14 m
• For silver, he found d 2 x 10-14 m
• Such small lengths are often expressed in
  femtometers where 1 fm 10-15 m
• Also called a fermi

Active Figure Rutherford Scattering
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Size and Density of Nuclei

• Since the time of Rutherford, many other
  experiments have concluded
• Most nuclei are approximately spherical
• Average radius is
• ro 1.2 x 10-15 m or 1.2 fm

• The volume of the nucleus (assumed to be
  spherical) is directly proportional to the total
  number of nucleons
• This suggests that all nuclei have nearly the
  same density
• Nucleons combine to form a nucleus as though they
  were tightly packed spheres

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Nuclear Stability

• Very large Coulomb repulsive forces exist between
  the charged protons in the nucleus the nucleus
  should fly apart
• Nuclei are stable because of the presence of
  another, short-range force, between nucleons
  called the nuclear force
• Light nuclei are most stable if N Z
• Heavier nuclei are most stable when N gt Z
• As the number of protons increase, the Coulomb
  force increases and more nucleons are needed to
  keep the nucleus stable
• No nuclei are stable when Z gt 83

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Binding Energy

• The total energy of the bound system (the
  nucleus) is less than the combined energy of the
  separated nucleons
• This difference in energy is called the binding
  energy of the nucleus
• It can be thought of as the amount of energy you
  need to add to the nucleus to break it apart into
  separated protons and neutrons

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Binding Energy per Nucleon

• Except for light nuclei, the binding energy is
  8 MeV per nucleon
• The curve peaks in the vicinity of A 60
• Nuclei with mass numbers greater than or less
  than 60 are not as strongly bound as those near
  the middle of the periodic table
• The curve is slowly varying at A gt 40

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Radioactivity

• Radioactivity is the spontaneous emission of
  radiation
• Experiments suggested that radioactivity was the
  result of the decay, or disintegration, of
  unstable nuclei 3 types
• Alpha particles
• The particles are 4He nuclei
• Beta particles
• The particles are either electrons or positrons
• A positron is the antiparticle of the electron
• It is similar to the electron except its charge
  is e
• Gamma rays
• The rays are high energy photons

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The Decay Constant

• The number of particles that decay in a given
  time is proportional to the total number of
  particles in a radioactive sample
• ?N -? N ?t
• ? is called the decay constant and determines
  the rate at which the material will decay
• The decay rate or activity, R, of a sample is
  defined as the number of decays per second

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Decay Curve

• The half-life is also a useful parameter
• Defined as the time it takes for half of any
  given number of radioactive nuclei to decay
• The decay curve follows the equation

Active Figure Radioactive Decay
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Decay Units and General Rules

• The unit of activity, R, is the Curie, Ci
• 1 Ci 3.7 x 1010 decays/second
• The SI unit of activity is the Becquerel, Bq
• 1 Bq 1 decay / second
• Therefore, 1 Ci 3.7 x 1010 Bq
• When one element changes into another element,
  the process is called spontaneous decay or
  transmutation
• Conservation of charge, mass-energy, and momentum
  must hold in radioactive decay

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Alpha Decay

• When a nucleus emits an alpha particle it loses
  two protons and two neutrons
• N decreases by 2
• Z decreases by 2
• A decreases by 4
• Symbolically
• X is called the parent nucleus
• Y is called the daughter nucleus

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Alpha Decay Example

• Decay of 226 Ra
• Half life for this decay is 1600 years
• Excess mass is converted into kinetic energy
• Momentum of the two particles is equal and
  opposite

Active Figure Alpha Decay of Radium-226
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Beta Decay

• Beta decay a neutron is transformed into a
  proton, and an electron and antineutrino are
  emitted
• A stays the same, Z ? Z1
• Beta decay a proton is transformed into a
  neutron, and a positron and neutrino are emitted
• A stays the same, Z ? Z1
• Symbolically
• Energy must be conserved
• ? is the symbol for the neutrino (carries away
  excess KE)
• ? is the symbol for the antineutrino (carries
  away excess KE)

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Beta Decay Example

• Radioactive Carbon-14 decay
• Used to date organic samples

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Gamma Decay

• Gamma rays are given off when an excited nucleus
  falls to a lower energy state
• Similar to the process of electron jumps to
  lower energy states and giving off photons
• The photons are called gamma rays, very high
  energy relative to light
• The excited nuclear states result from jumps
  made by a proton or neutron
• The excited nuclear states may be the result of
  violent collision or more likely of an alpha or
  beta emission

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Gamma Decay Example

• Example of a decay sequence
• The first decay is a beta decay emission
• The second step is a gamma decay emission
• C indicates the Carbon nucleus is in an excited
  state
• Gamma emission doesnt change either A or Z

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Medical Applications of Radiation

• Tracing
• Radioactive particles can be used to trace
  chemicals participating in various reactions
• Example, 131I to test thyroid action
• Sterilization
• Radiation has been used to sterilize medical
  equipment
• Used to destroy bacteria, worms and insects in
  food
• Bone, cartilage, and skin used in graphs is often
  irradiated before grafting to reduce the chances
  of infection

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Medical Applications of Radiation

• CAT scans
• Computed Axial Tomography
• Produces pictures with greater clarity and detail
  than traditional x-rays

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Medical Applications of Radiation

• MRI scans
• Magnetic Resonance Imaging
• When a nucleus having a magnetic moment is placed
  in an external magnetic field, its moment
  precesses about the magnetic field with a
  frequency that is proportional to the field
• Transitions between energy states can be detected
  electronically to produce cross-sectional images

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Medical Applications of Radiation

• 3D-CRT Treatment
• Three-dimensional conformal radiation therapy
  uses sophisticated computers, CT scans and/or MRI
  scans to create detailed 3-D representations of a
  tumor and surrounding organs
• Radiation beams are then shaped exactly to treat
  the size and shape of the tumor nearby normal
  tissue receives less radiation exposure

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3D-CRT Treatment Planning