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Half-Life
Introduction
During the half-life, half of the atoms decay and the other half remain
undecayed. Remember, when it decays, it changes but does not disappear.
Carbon-14 is used to date objects that lived at one time. It dates
from when they died.
Uranium-238 is used to date rocks.
How many atoms of each isotope remain after 145.5 seconds if you began with
10,000,000 atoms of oxygen19 ?
|
Problem
Solving Process |
| 1. |
Look up the
half-life and the type of decay on
the chart .
|
| 2. |
Determine the
isotope produced by the decay.
|
| 3. |
Make a chart with
the following information.
|
|
a. |
Start with a time of 0 and added the half-life time for each row.
|
|
b. |
Start with the initial number of atoms of the beginning isotope. Divide
by 2 for each row.
|
|
c. |
Start with 0 atoms for the isotope formed. The total number of atoms
remains unchanged. Thus initial atoms - decayed atoms = undecayed atoms.
|
|
d. |
Stop at the point indicated by the problem. This can be a time, number
of half-lifes, or number of atoms. |
Oxygen-19 has a half-life of 29.1
seconds and undergoes a beta decay.
|
Beta Decay Oxygen-19
|
Time
(sec) |
Oxygen-19
(Million Atoms) |
Fluorine-19
(Million Atoms)
|
|
0.0
|
10.000
|
0.000
|
|
29.1
|
5.000
|
5.000
|
|
58.2
|
2.500
|
7.500
|
|
87.3
|
1.250
|
8.750
|
|
116.4
|
0.625
|
9.375
|
|
145.5
|
0.312
|
9.688
|
Graphing the information allows you to interpret between
half-lifes. The above graph shows that 4,000,000 atoms of oxygen-19 remain
after 38 seconds.
Table of Contents
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Half-life
Problems
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| 1. |
How much time is necessary for
1,875,000 atoms to decay if you began with 2,000,000 atoms of cesium-129
?
|
| 2. |
How much time has passed if 500,000 atoms
of uranium-227
remain if you began with 4,000,000 atoms of uranium-227 ?
|
| 3. |
How many atoms of each isotope remain
after 14.25 years if you began with 6,000,000 atoms of plutonium-236
?
|
| 4. |
How much time is necessary for the
formation of 11,625,000 atoms of gallium-71 if you began with 12,000,000 atoms
of zinc-71? |
Table of Contents
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Half-Life
Answers
|
| 1. |
How much time is necessary for
1,875,000
atoms to decay if you began with 2,000,000 atoms of cesium-129 ?
Problem Solving Process
|
|
Time
(hours)
0.0
32.1
64.2
96.3
128.4 |
Cesium-129
(atoms)
2,000,000
1,000,000
500,000
250,000
125.000 |
Xenon-129
(atoms)
0
1,000,000
1,500,000
1,750,000
1,875,000 |
The
beta decay of cesium-129 produces xenon-129 with a half-life of
32.1 hours.
Time always starts with 0.
Half-life is added each step.
Atoms of cesium-129 was cut in half each
step.
2,000,000 atoms - atoms cesium-129
determines atoms of xenon-129
We stopped when the xenon-129 column
reached 1,875,000. The xenon-129 column represents the decayed
atoms. |
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|
|
|
| 2. |
How much time has passed if 500,000 atoms
of uranium-227 remain if you began with
4,000,000 atoms of uranium-227 ? Problem Solving Process
|
|
Time
(minutes)
0.0
1.3
2.6
3.9 |
Uranium-227
(atoms)
4,000,000
2,000,000
1,000,000
500,000 |
Thorium-223
(atoms)
0
2,000,000
3,000,000
1,500,000 |
The alpha decay
of uranium-227 produces thorium-223 with a half-life of 1.3 minutes.
Time always starts with 0.
Half-life is added each step.
Atoms of uranium-227 was cut in half
each step.
4,00,000 atoms - atoms uranium-227
determines atoms of thorium-223
We stopped when the uranium-227 column
reached 500,000. The uranium-227 column represents the
undecayed atoms. |
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|
|
|
| 3. |
How many atoms of each isotope remain
after 14.25 years if you began with 6,000,000 atoms of plutonium-236
? Problem Solving Process
|
|
Time
(years)
0.00
2.85
5.70
8.55
11.40
14.25 |
Plutonium-236
(atoms)
6,000,000
3,000,000
1,500,000
750,000
375,000
187,500 |
Uranium-232
(atoms)
0
3,000,000
4,500,000
5,250,000
5,625,000
5,812,500 |
The alpha decay of
plutonium-236 produces uranium-232 with a half-life of 2.85 years.
Time always starts with 0.
Half-life is added each step.
Atoms of plutonium-236 was cut in half
each step.
6,00,000 atoms - atoms plutonium-236
determines atoms of uranium-232
We stopped when the time column reached
14.25 years. |
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|
|
|
| 4. |
How much time is necessary for the
formation of 11,625,000 atoms of gallium-71 if you began with 12,000,000 atoms
of zinc-71?
Problem Solving Process |
|
Time
(minutes)
0
2.4
4.8
7.2
9.6
12.0 |
Zinc-71
(atoms)
12,000,000
6,000,000
3,000,000
1,500,000
750,000
375,000 |
Gallium-71
(atoms)
0
6,000,000
9,000,000
10,500,000
11,250,000
11,625,000 |
The beta decay of zinc-71
produces gallium-71 with a half-life of 2.4 minutes.
Time always starts with 0.
Half-life is added each step.
Atoms of zinc-71 was cut in half each
step.
12,000,000 atoms - atoms zinc-71
determines atoms of gallium-71
We stopped when the gallium-71 column
reached 11,625,000. The gallium-71 column represents the
decayed atoms. |
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Table of Contents
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Radioactive
Decays
|
| Isotope |
Half-life |
Type of Decay
|
|
oxygen-19 |
29.1
s |
Beta |
|
fluorine-20 |
11.6
s |
Beta |
|
silicon-26 |
2.1
s |
Positron |
|
zinc-71 |
2.4
m |
Beta |
|
cesium-129 |
32.1
h |
Electron
Capture |
|
promethium-149 |
53.1
h |
Beta |
|
gadolinium-145 |
25
m |
Positron |
|
osmium-183 |
12.0
h |
Electron
Capture |
|
lead-212 |
10.6
h |
Beta |
|
plutonium-236 |
2.85
y |
Alpha |
|
selenium-84 |
3.2
m |
Beta |
|
uranium-227 |
1.3
m |
Alpha |
|
polonium-210 |
138
d |
Alpha |
|
chlorine-39 |
55.5
m |
Beta |
|
scandium-49 |
57.5
m |
Beta |
|
hydrogen-3 |
12.3
y |
Beta |
Table of Contents |
