Nuclear Stability and Decay

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Nuclear Stability and Decay

• More than 1500 different isotopes are known. Of
  those, only 264 are stable and do not decay over
  time.
• One factor that affects the stability of nucleus
  is the ratio of neutrons to protons.
• Too many or too few neutrons relative to the
  number of protons makes the nucleus unstable.
• A neutron vs proton plot of stable nuclei form a
  pattern called the band of stability.

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Band of Stability
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• For elements with atomic numbers 20 or less, this
  ratio is about 11. Above atomic number 20,
  stable nuclei have more neutrons than
  protons.
• The band of stability can be explained by the
  relationship between the nuclear force and the
  electrostatic forces between protons.
• As the number of protons in a nucleus increases,
  the repulsive electrostatic force between protons
  increases faster than the nuclear force.
• More neutrons are required to increase the
  nuclear force and stabilize the nucleus.
• Beyond the atomic number 83, bismuth, the
  repulsive force of the protons is so great
  that no stable isotopes
  exists.

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Half-Life

• Every radioisotope has a characteristic rate of
  decay, which is measured by its half-life.
• Half-life is the time required for one-half of
  the nuclei in a radioisotope sample to decay.
• During each half-life, half of the remaining
  radioactive atoms decay into atoms of a new
  element.
• Each radioactive nuclide has its own half-life.
  Half-lives can be a short as a fraction of a
  second or as long as billions of years.

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• One isotope that has a long half-life is
  uranium-238.
• 4.5 billion years
• decays through a complex series of unstable
  isotopes to the stable isotope of lead-206.

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Decay Series of U-238
Stable Isotope
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• The following equation can be used to calculate
  how much of an isotope will remain after a given
  number of half-lives.
• A Ao x (1/2)n
• A stands for the amount remaining, Ao for the
  initial amount, and n for the number of
  half-lives.

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Half-Life Sample Problem

• Phosphorus-32 has a half-life of 14.3 days.
• How long is four half-lives?
• If you started with 24.0 g of phosphorus-32, how
  many grams of the isotope remain at the end four
  half-lives?

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Outcome Sentences

• After reflecting on todays lesson, complete
  three of the sentence starters.

• Sentence Starters
• Ive learned
• I was surprised
• Im beginning to wonder
• I would conclude
• I now realize that