Radioactive Decay

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Radioactive Decay

• The number of atoms in a sample that decay
  depends on the total number of atoms in the
  sample!!
• This fact yields a rate of decay called an
  exponential decay
• Exponential decay has a simple picture

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Exponential Decay
Decay of 226Ra
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Half-Life

• There are a large range of half-lives seen in
  nature
• Half-lives are unaffected by the nucleis
  surroundings and only depend on what goes on
  inside the nucleus
• 238U has a half-life of 4.5 billion years

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Half-Life

• To summarize, one-half of the sample will decay
  in one half-fife
• One-half of that one-half will decay in the next
  half life
• One-half of that one-fourth will decay in the
  next half life

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Half-Life
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Transmutations

• The changing of one element to another is called
  transmutation
• This occurs whenever there is an alpha decay or a
  beta decay
• Remember, that for a gamma decay, the nucleus
  just changes internal energy levels, but doesnt
  change the identity of nucleons

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Transmutations

• Consider an alpha decay
• 238U - 234Th alpha (4He)
• Have to count the number of protons and neutrons
• Protons U-92, Th-90, He-2 Balance!!
• Neutrons U-146, Th-144, He-2 Balance!!
• Mass No. U-238, Th-234, He-4 Balance!!

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Transmutations

• Consider a beta decay
• 234Th - 234Pa beta
• This means a neutron changed into a proton
• So mass number stays the same
• Proton number increases by one and the thorium
  changes into protactinium
• Actually an anti-neutrino appears also

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Transmutations
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Artificial Transmutation

• First example was Rutherford bombarding nitrogen
  with alpha particles
• 4He 14N - 17O 1H
• He viewed the reaction with a cloud chamber
• The particles left a vapor trail in the mist

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Cloud Chamber
When you pull the piston down suddenly, you
reduce the air pressure in the chamber. This
means vapor is now super-saturated. A charged
particle acts as a nucleation seed to condense
the liquid from the vapor. This is the same
principle as cloud-seeding to make it rain.
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Isotopic Dating

• Cosmic rays (mostly high energy protons) strike
  upper atmosphere and cause transmutations that
  result in many protons and neutrons being sprayed
  out
• Protons tend to grab electrons from other atoms
  and become simple hydrogen
• Neutrons keep going and smash into other atoms

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Isotopic Dating

• When a neutron strikes nitrogen
• 1n 14N - 14C 1H
• In the atmosphere, 14C is about 1 part in 1011
• Reacts with plants just like 12C
• 14C decays via beta emission
• 14C - 14N beta half life of 5730 years

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Carbon Dating

• When a plant dies, it stops the intake of carbon
• Since the 14C decays, after 5730 years, half of
  it will be gone
• We can just weigh a piece of dead wood, calculate
  how much 14C it originally had and measure to how
  much it has now to get the age

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Uranium Dating

• We know the half -life of 238U and 235U
• They have series that end in 206Pb and 207Pb
• Compare how much U vs. special lead and calculate
  the age of the rock!!
• Carbon dating only good for about 50,000 years
• Uranium rock dating good for millions of years

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Nuclear Fission
1n 235U - 91Kr 142Ba 31n
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Chain Reaction
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Chain Reaction

• The key to keeping the reaction going is that at
  least one of the neutrons given off, must cause
  another fission
• Controlled reaction in a nuclear reactor
• If two or three cause fissions, you can get a
  bomb!
• Idea of critical mass

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Critical Mass
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Atom Bomb
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Nuclear Reactor
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Mass-Energy Relationship

• Einsteins famous equation E mc2
• A nucleus is measured to have less mass than the
  sum of its parts
• 12C has a mass exactly 12.00000 amu
• Six protons have mass 6 x 1.00728 amu
• Six neutrons have mass 6 x 1.00867 amu
• Parts have mass 12.09570 amu

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Mass-Energy Relationship

• So, where does the mass go?
• It is the binding energy that is holding the
  nucleus together
• Interesting to look at the mass per nucleon as we
  change the atomic number (change which element we
  look at)

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Mass-Energy Relationship
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Nuclear Fission
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Nuclear Fusion
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Nuclear Energy
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Fusion Reactions