1. The shorter the half-life, the faster the decay rate.
A half life can be used to compare the rate of radioactive decay for an isotope.
The shorter the half-life, the faster the decay rate.
All radioactive decay rates follow a similar pattern called a decay curve.
The difference between the different isotopes is the length of their half-lives.
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2. Geologic Dating
Methuselah: World’s Oldest Tree ~4780 years old.
Gorgosaurus ~75 million years old.
What are some ways you know to discover how old each depicted organism is? Difficult to tell age from just looking:
-Tree ring analysis.
-Relative Dating: Dinosaurs are older than humans.
-Absolute Dating: Decay of isotopes to give a numerical age.
It can be difficult to determine the ages of objects by sight alone.
Radioactivity provides a method to determine age by measuring relative amounts of remaining radioactive material to stable products formed.
radioactive isotopes decay into a stable atom over time.
This decay rate is not affected by environmental factors and is always consistent.
Carbon dating measures the ratio of carbon-12 and carbon-14.
Stable carbon-12 and radioactive carbon-14 exist naturally in a constant ratio.
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3. Determining Age with Carbon Dating
Radioactive isotopes decay into a stable atom over time.
We can measure relative amounts of remaining radioactive material to the stable products that are formed.
This decay rate is not affected by environmental factors and is always consistent.
Carbon dating measures the ratio of carbon-12 and carbon-14.
Stable carbon-12 and radioactive carbon-14 exist naturally in a constant ratio.
See pages
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4. equal proportions of carbon-14 and carbon-12 by eating plants.
Carbon Dating
All animals obtain
equal proportions of carbon-14
and carbon-12 by eating plants.
However, when the organism
dies carbon-14 radioactively decays
into nitrogen-14 at a fixed rate
without being replaced (no more
plants are ingested).
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5. This means that the ratio of carbon-14 to carbon-12 changes.
Decay
This means that the ratio of
carbon-14 to carbon-12 changes.
By measuring this ratio, we can
determine the age of the organic
remains.
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6. Carbon Dating
Carbon dating only works for organisms less than years old. Using carbon dating, these cave paintings of horses, from France, were drawn years ago.
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7. The Rate of Radioactive Decay
Half-life measures the rate of radioactive decay.
Half-life = time required for half of the radioactive sample to decay.
is a constant rate of decay.
Strontium-90 has a half-life of 29 years. If you have 10 g of strontium-90 today, there will be 5.0 g remaining in 29 years.
Decay curves show the rate of decay for radioactive elements.
The curve shows the relationship
between half-life and percentage of
original substance remaining.
See pages
The decay curve for strontium-90
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8. There are many radioisotopes that can be used for dating.
Common Isotope Pairs
There are many radioisotopes that can be used for dating.
Parent isotope = the original, radioactive material
Daughter isotope = the stable product of the radioactive decay
The rate of decay remains constant, but some elements require one step to decay while others decay over many steps before reaching a stable daughter isotope.
Carbon-14 decays into nitrogen-14 in one step.
Uranium-235 decays into lead-207 in 15 steps.
Thorium-235 decays into lead-208 in 10 steps.
See page 307
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9. The Potassium-40 Clock
Radioisotopes with very long half-lives can help determine the age of very old things.
The potassium-40/argon-40 clock has a
half-life of 1.3 billion years.
Argon-40 produced by the decay of
potassium-40 becomes trapped in rock.
Ratio of potassium-40 : argon-40
shows age of rock.
See pages
Take the Section 7.2 Quiz
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10. a) Radioactive isotope decay is measured as a half-life.
Here’s how it works:
a) Radioactive isotope decay is measured as a half-life.
One half-life is equal to the amount of time required for half of the parent isotope present in a sample to decay into the daughter isotope. This length of time varies depending on the parent isotope being analyzed.
b) By multiplying the half-life time for the parent isotope by the number of half-lives elapsed, you can determine how old the sample is.
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11. Radioactive Decay of Potassium-40
The Potassium-40 Clock is the use of this radioactive isotope’s half-life to determine the age of very old rocks.
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12. Radioactive Decay of Potassium-40
a) Using the Potassium-40 decay curve, determine the age of a rock with 25% Potassium-40 and 75% Argon-40.
b) What is ratio of argon-40 to potassium-40 remains 3.9 billion years after the rock has formed?
*Complete Check Your Understanding Questions 6, 7, 9-12 on page 311.
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13. Radioactive Decay of Potassium-40
a) Using the Potassium-40 decay curve, determine the age of a rock with 25% Potassium-40 and 75% Argon-40.
25% Potassium-40 = 2 half-lives
2 x 1.3 billion years = 2.6 byo.
b) What is ratio of argon-40 to potassium-40 remains 3.9 billion years after the rock has formed?
*Complete Check Your Understanding Questions 6, 7, 9-12 on page 311.
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14. Radioactive Decay of Potassium-40
a) Using the Potassium-40 decay curve, determine the age of a rock with 25% Potassium-40 and 75% Argon-40.
25% Potassium-40 = 2 half-lives
2 x 1.3 billion years = 2.6 byo.
b) What is ratio of argon-40 to potassium-40 remains 3.9 billion years after the rock has formed?
3.9b / 1.3 b = 3 Half-Lives = 12.5% parent isotope remains
1000g x = 125 g
*Complete Check Your Understanding Questions 6, 7, 9-12 on page 311.
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15. -How many half-lives have elapsed since the Rhino died?
Example 1
An archaeologist finds a Woolly Rhinoceros and through testing discovers that of the carbon present in the skeleton, 25% is carbon-14.
-How many half-lives have elapsed since the Rhino died?
-What is the time required for one half-life to elapse for carbon-14?
-How long ago did the Rhino die?
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16. -How many half-lives have elapsed since the Rhino died? 2
Example
For example, an archaeologist finds a Woolly Rhinoceros and through testing discovers that of the carbon present in the skeleton, 25% is carbon-14.
-How many half-lives have elapsed since the Rhino died? 2
-What is the time required for one half-life to elapse for carbon-14?
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17. -How many half-lives have elapsed since the Rhino died? 2
Example
For example, an archaeologist finds a Woolly Rhinoceros and through testing discovers that of the carbon present in the skeleton, 25% is carbon-14.
-How many half-lives have elapsed since the Rhino died? 2
-What is the time required for one half-life to elapse for carbon-14?
5730 years
-How long ago did the Rhino die?
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18. -How many half-lives have elapsed since the Rhino died? 2
Example
For example, an archaeologist finds a Woolly Rhinoceros and through testing discovers that of the carbon present in the skeleton, 25% is carbon-14.
-How many half-lives have elapsed since the Rhino died? 2
-What is the time required for one half-life to elapse for carbon-14?
5730 years
-How long ago did the Rhino die?
5730 x 2 = 11,460 years ago.
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19. Example 2
If a Neanderthal skeleton starts with 1000 grams of carbon-14, how much would remain 17,190 years after the organism died?
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20. a) How many half-lives have elapsed?
b) What percentage of the parent isotope remains?
c) After 17,190 yrs, how much of the parent isotope is remaining?
d) How many grams of Nitrogen-14 have been produced over 17,190 years of Carbon-14’s radioactive decay?
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21. a) How many half-lives have elapsed? 17,190 / 5,730 = 3 half-lives
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22. b) What percentage of the parent isotope remains? 12.5% (½ x ½ x ½)
c) After 17,190 yrs, how much of the parent isotope is remaining?
1000 x = 125 grams of Carbon-14 after 17,190 years (or 3 half-lives)
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23. b) What percentage of the parent isotope remains? 12.5% (½ x ½ x ½)
c) After 17,190 yrs, how much of the parent isotope is remaining?
1000 x = 125 grams of Carbon-14 after 17,190 years (or 3 half-lives)
d) How many grams of Nitrogen-14 have been produced over 17,190 years of Carbon-14’s radioactive decay?
1000 g – 125g = 875 grams of Nitrogen-14
1000 grams x = 875 grams of Nitrogen-14
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24. e) What percentage of the Carbon-14 is remaining after 2 half-lives?
f) What is the ratio of Carbon-14 to Nitrogen-14 after 4 half-lives?
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25. e) What percentage of the Carbon-14 is remaining after 2 half-lives?
25%
f) What is the ratio of Carbon-14 to Nitrogen-14 after 4 half-lives?
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26. e) What percentage of the Carbon-14 is remaining after 2 half-lives?
25%
f) What is the ratio of Carbon-14 to Nitrogen-14 after 4 half-lives?
Four half-lives: 6.25% Carbon-14 remaining, 93.75% N-14 formed
If we knew the mass of the sample, we would multiply…
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27. *Complete Check Your Understanding Questions 6, 7, 9-12 on page 311.
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