Half-Life and Radioisotope Dating

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Half-Life and Radioisotope Dating
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Rate of Decay

• The measurement of the time required for a
  radioactive material to decay is called its
  half-life.
• This is the time required for half of the
  nuclides in a sample to decay.
• Half-life of 238U is 4.5 billion years
• Half-life of 131I is 8.07 days
• Half-life of 194Po is 0.7 second

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Carbon-14 Dating

• We have some radioactive materials in our bodies.
  
• One of the isotopes is carbon-14.
• Carbon-14 is an isotope of the carbon in CO2.
• All living things take it in during respiration.

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Carbon-14 Dating

• Scientist use carbon-14 to date very old things.

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Carbon-14 Dating

• Decayed carbon-14 is continually being replaced
  in the body.
• Once the organism dies the carbon-14 is no longer
  replaced, but what is there continues to decay.
• By examining the amount of carbon-14 left in the
  material, scientist can estimate the age of the
  subject.
• Accurate to about 20,000-50,000 years.

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Practice Problems

• 1) A fossilized tree killed by a volcano was
  studied. It had 6.25 percent of the amount of
  carbon-14 found in a sample of the same size from
  a tree that is alive today. When did the
  volcanic eruption take place?

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Practice Problems

• You need to find out how many times ½ (0.5) must
  be used as a factor to produce 0.0625.
• The answer is 4 times because
• 0.5 X 0.5 X 0.5 X 0.5 0.0625
• 4 half-lives have gone by and each half-life is
  5730 years.
• 5730 years X 4 22,920 years

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Practice Problems

• 2) A rock was analyzed using potassium-40. The
  half-life of potassium-40 is 1.25 billion years.
  If the rock had only 25 percent of the
  potassium-40 that would be found in a similar
  rock formed today, calculate how long ago the
  rock was formed.
• Potassium-40 Half-life is 1.25 billion years

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Practice Problems

• 2) Convert 25 to a decimal ---
• 0.5 X 0.5 0.25
• 2 half-lives have gone by.
• 1.25 billion X 2 2.50 billion years

0.25
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Practice Problems

• 3) Ash from an early fire pit was found to have
  12.5 percent as much carbon-14 as would be found
  in a similar sample of ash today. How long ago
  was the ash formed?
• Convert 12.5 to a decimal ---
• 0.5 X 0.5 X 0.5 0.125
• 3 half-lives have gone by.
• 5730 X 3 17,190 years ago

0.125
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Practice Problems

• 4) A rock sample has 12.5 of the potassium-40
  that would be present in a similar rock formed
  today. How old is the rock sample?
• Convert 12.5 to a decimal ---
• 0.5 X 0.5 X 0.5 0.125
• 3 half-lives have gone by.
• 1.25 billion X 3 3.75 billion years old

0.125
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Practice Problems

• 5) How old is a piece of wood in which the
  carbon-14 is 3.12 of that in wood formed today?
• Convert 3.12 to a decimal ---
• 0.5 X 0.5 X 0.5 X 0.5 X 0.5 0.03125
• 5 half-lives have gone by.
• 5730 X 5 28,650 years old

0.0312
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Half-life equation

• Amount remaining amount of original sample
  2n
• n number of half-lives

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• An isotope of cesium (cesium-137) has a half-life
  of 30 years. If 1.0 mg of cesium-137
  disintegrates over a period of 90 years, how many
  mg of cesium-137 would remain?

amount of original sample
1.0 mg
Amount remaining
2n
23
1 half life
30 years
Therefore, 90 years is equal to how many half
lives?
n 3
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4. Sodium-25 was to be used in an experiment,
but it took 3.0 minutes to get the sodium from
the reactor to the laboratory. If 5.0 mg of
sodium-25 was removed from the reactor, how many
mg of sodium-25 were placed in the reaction
vessel 3.0 minutes later if the half-life of
sodium-25 is 60 seconds?
amount of original sample
Amount remaining
5.0 mg
23
2n
1 half life
60 seconds
Therefore, 3 minutes is equal to how many half
lives?
n 3