1. 7.2 What is Half Life?
Half Life is the time required for half of the radioactive sample to decay.
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2. Strontium-90 has a half-life of 29 years.
Half-life is constant for any radioisotope and can be used to measure the rate of radioactive decay for that isotope.
Strontium-90 has a half-life of 29 years.
If you have 100 g of strontium-90 today, there will be 50 g remaining in 29 years.
Different isotopes have different rates of decay and therefore different half-lives.
The shorter the half-life, the faster the decay rate.
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3. Half-life
All radioactive decay rates follow a similar pattern called a decay curve
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4. Uses for Half Life: Geologic Dating
Geological dating is a method of determining the age of rocks and fossils by measuring the radioactive decay radioactive isotopes embedded in the rocks.
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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5. Determining Age with Carbon Dating
Radioactive isotopes decay into stable atoms over time. We can measure relative amounts of remaining radioactive material to the stable products that are formed.
By measuring this ratio, we can determine the age of the organic remains.
See pages
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6. Carbon Dating
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7. Carbon dating measures the ratio of carbon-12 and carbon-14.
Stable carbon-12 and (unstable) radioactive carbon-14 exist naturally in a constant ratio.
All animals obtain equal proportions of carbon-14 and carbon-12 by eating plants.
When the organism dies, Carbon-12, being stable, remains unchanged while unstable, radioactive carbon-14 decays into nitrogen-14 at a fixed rate.
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8. As neither carbons are being replenished, the ratio of
Carbon Dating
As neither carbons are being replenished, the ratio of
carbon-14 to carbon-12 changes.
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9. Carbon dating only works for organisms less than 50 000 years old.
Using carbon dating, these cave paintings of horses,
from France, were drawn years ago.
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10. Rate of Radioactive Decay
Decay curve is the graph showing the rate of decay of a radioisotope
The decay curve for strontium-90
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11. After each half-life, amount of radioisotope drops by half.
Decay Curve
After each half-life, amount of radioisotope drops by half.
The curve shows the relationship between half-life and percentage of original substance remaining.
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12. Iodine-131 is used for treating thyroid cancer
Decay Curve Example
Iodine-131 is used for treating thyroid cancer
It has a half-life of 8 days
Suppose you have 20g of iodine-131
You can find out how much will remain after 16:
16 days = 2 half-lives
20g x ½ x ½ = 5
See pages
The decay curve for strontium-90
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13. Decay Curve Practice Do Practice Problems p306
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14. Many radioisotopes can be used for dating.
Common Isotope Pairs
Many radioisotopes can be used for dating.
Isotope that decays is called the Parent isotope
Stable product(s) of parent isotope’s decay is called Daughter isotope.
See page 307
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15. Carbon-14 decays into nitrogen-14 in one step.
Common Isotope Pairs
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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16. Potassium-40 has a half life of 1.3 billion years.
The Potassium-40 Clock
Radioisotopes with very long half-lives can help determine the age of very old things.
Potassium-40 has a half life of 1.3 billion years.
Its daughter isotope is argon-40.
When rock is created from lava, the daughter isotope argon-40 is forced out leaving only the parent potassium-40.
(the rock is starting with 0% daughter, 100% parent)
See pages
Take the Section 7.2 Quiz
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17. The Potassium-40 Clock
Over time the potassium-40 decays and creates argon-40 which remains trapped in the rock.
As the amount of potassium-40 decreases, the amount of argon-40 increases.
Using the graph and the ratio of potassium-40 to argon-40 scientists can find how old the rock is.
See pages
Take the Section 7.2 Quiz
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18. Since these rocks were probably formed at the beginning of the earth’s life, the age of the rock is close to the age of the earth.
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19. Check your understanding
Which two isotopes get compared in radiocarbon dating?
What is used to measure readioactive decay rate?
Does a half-life change for a given radioisotope?
What is a decay curve?
What is the daughter isotope of uranium-235
What happens to the amount of argon-40 as the amount of potassium-40 decreases?
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20. Check your understanding
Carbon-12 and carbon-14
Half-life No
A graph of the ddecay of a radioisotope
Lead-207
The amount of argon-40 increases
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21. Crash Course: Nuclear Chemistry
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22. 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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23. 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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24. 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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25. -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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26. -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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27. -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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28. -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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29. 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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30. 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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31. a) How many half-lives have elapsed? 17,190 / 5,730 = 3 half-lives
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32. 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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33. 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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34. 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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35. 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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36. 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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