Name ____________________________________________ Date ____________________ Blk___ NB#______
Nuclear Chemistry: Half-Lives and Radioactive Dating
Scientists look at half-life decay rates of radioactive isotopes to estimate when a particular atom might decay.
A useful application of half-lives is radioactive dating. This has to do with figuring out the age of ancient things.
1. Why is radioactive dating useful?
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If you could watch a single atom of a radioactive isotope, U-238, for example, you wouldn’t be able to predict
when that particular atom might decay. It might take a millisecond, or it might take a century. There’s simply
no way to tell. But if you have a large enough sample, a pattern begins to emerge. It takes a certain amount of
time for half the atoms in a sample to decay. It then takes the same amount of time for half the remaining
radioactive atoms to decay, and the same amount of time for half of those remaining radioactive atoms to
decay, and so on. This process is shown in the following table.
2. What two factors are necessary to determine the radioactive decay process? _______________________
_______________________
Half-Life Decay of a Radioactive Isotope
Half-Life
Percent of Radioactive
The amount of time it takes for one-half of a sample to decay is
called the half-life of the isotope.
Isotope Remaining
3. What is the amount of time it takes to for a radioactive
sample to decay called?
0
100.00
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1
50.00
2
25.00
3
12.50
4
6.25
5
3.12
6
1.56
7
0.78
8
0.39
9
0.19
10
0.09
It’s important to realize that the half-life decay of radioactive
isotopes is not linear. For example, you can’t find the remaining
amount of an isotope as 7.5 half-lives by finding the midpoint
between 7 and 8 half-lives. This decay is an example of an
exponential decay.
4. What term is used to describe the rate of decay for a radioactive isotope?
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Safe handling of radioactive material
Knowing about half-lives is important because it enables you to determine when a sample of radioactive
material is safe to handle. The rule is that a sample is safe when its radioactivity has dropped below detection
limits. And that occurs at 10 half-lives. So, if radioactive iodine-131 (which has a half-life of 8 days) is injected
into the body to treat thyroid cancer, it’ll be “gone” in 10 half-lives, or 80 days.
5. Flourine-18 has a half-life of about 110 minutes. How many minutes would it be before it was
considered “gone”? hours? Show Work!!
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Radioactive dating
Radioactive dating is helpful for figuring out the age of ancient things. Carbon-14 (C-14), a radioactive isotope
of carbon, is produced in the upper atmosphere by cosmic radiation. The primary carbon-containing
compound in the atmosphere is carbon dioxide, and a very small amount of carbon dioxide contains C-14.
Plants absorb C-14 during photosynthesis, so C-14 is incorporated into the cellular structure of plants. Plants
are then eaten by animals, making C-14 a part of the cellular structure of all living things. As long as an
organism is alive, the amount of C-14 in its cellular structure remains constant. But when the organism dies,
the amount of C-14 begins to decrease. Scientists know the half-life of C-14 (5,730 years), so they can figure
out how long ago the organism died.
Carbon-14 dating can only be used to determine the age of something that was once alive. It can’t be used to
determine the age of a moon rock or a meteorite. For nonliving
Substance
substances, scientists use other isotopes, such as potassium-40.
Half lives
Remaining
0
703
6. The half-life of plutonium
100
351.5
n bone is about 100 years. If
200
175.75
a bone specimen has 703
300
87.875
grams of plutonium in it,
400
43.9375
how much will remain after
500
21.96875
700 years?
600
10.984375
___________________
700
5.4921875
7. Why would ALL radiometric graphs have the same basic
shape?
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Parent
Daughter
Half Life (years)
Dating Range
(years)
Minerals/materials
238U
Uranium-238
206Pb
Lead-206
4.5 billion
10 million 4.6 billion
Minerals include zircon, uraninite.
Igneous or metamorphic rocks.
40K
Potassium-40
40Ar
Argon-40
1.3 billion
0.05 million 4.6 billion
Minerals include muscovite, biotite, Kfeldspar. Volcanic rocks.
87Rb
Rubidium-87
87Sr
Strontium-87
47 billion
10 million 4.6 billion
Minerals include muscovite, biotite, Kfeldspar. Igneous or metamorphic rocks.
100 - 70,000
years
Not used for dating rocks, except
carbonates from earth's surface such as
recent coral reefs. Used for young organic
materials, or surface-water samples:
Wood, charcoal, peat, bone, tissue,
carbonate minerals from surficial
environments, water containing dissolved
carbon.
14C
Carbon-14
14N
Nitrogen-14
5,730 years
8. The above chart shows some of the materials that can be used for radiometric dating. What does is
mean by “parent” material and “daughter” material?
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9. In the figure to the right, what is the status of the Potassium-40? And
the Argon-40?
Potassium-40 is _______________________________________________
Argon-40 is ___________________________________________________
10. How long does it take Potassium-40 to decay into Argon-40?
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11. The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how many grams
would be left after 7.2 minutes has elapsed?
How to find Solution:
7.2 / 2.4 = 3 half-lives
Find 3 half-lives on chart – 12.5
Convert percentage to decimal
12.5% = 0.125
100.0 g x 0.125 = 12.5 g remaining
Number of
Half Lives
0
1
2
3
4
5
6
Percentage of
Parent Material
100
50
25
12.5
6.25
3.125
1.5625
Percentage of
Daughter Material
0
50
75
87.5
93.75
96.875
98.4375
12. Os-182 has a half-life of 21.5 hours. If one had 200.0 g at the beginning, how many grams
would be left after 86 hours has elapsed?
13. How long will it take for a 40.0 gram sample of I-131 (half-life = 8.040 days) to decay to 3.125%
its original mass?
14. At time zero, there are 10.0 grams of W-187. If the half-life is 24 hours, how much will be
present at the end of one day? Two days? Seven days?
15. 100.0 grams of an isotope with a half-life of 36.0 hours is present at time zero. How much
time will have elapsed when 3.125 grams remains?