HalfLife of a Radioactive Element

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Half-Life of a Radioactive Element
2
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200
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190
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180
170
160
150
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140
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Half-Life is the time it takes half of the
split peas to turn to lima beans!
130
.
120
110
100
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Number of Atoms
90
.
It take 7 minutes for half of the split peas to
decay to lima beans!
80
70
60
50
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40
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30
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20
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10
0
7
5
10
20
30
40
0
15
25
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Time (min)
3
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200
.
190
.
180
170
160
150
.
How many split pea atoms would be left after 2
half-lives?
140
.
130
.
120
2 half-lives would be 14 minutes
110
100
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Number of Atoms
90
.
38 split peas or atoms would still be radioactive
after 2 half-lives!
80
70
60
50
.
40
.
30
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.
20
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10
0
7
5
10
20
30
40
0
15
25
35
Time (min)
4
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200
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190
.
180
170
160
150
.
How many split pea atoms would be left after 3
half-lives?
140
.
130
.
120
3 half-lives would be 21 minutes
110
100
.
Number of Atoms
90
.
18 split peas or atoms would still be radioactive
after 3 half-lives!
80
70
60
50
.
40
.
30
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20
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10
0
7
5
10
20
30
40
0
15
25
35
Time (min)
5
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The Fractions of Half-Life
of half-lives__________ fraction of initial
element still remaining
After 1 half-life there will be ½ of the initial
element, ex. Initial element 200g after 1
half-life 100g after 2 half-lives
50g after 3 half-lives 25g
after 4 half-lives 12.5g after 5
half-lives 6.25g after 6 half-lives
3.125g
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If 100.0 g of carbon-14 decays until only 25.0 g
of carbon-14 is left after 11,460 years, what is
the half-life of carbon-14?
1 4
final mass of the sample
25
half-life fraction

initial mass of the sample
100.0
According to your notes ¼ is the fraction for 2
half-lives.
X
amount of time 1 half-life
total time of decay
11,460

1
number of half-lives
2
2x 11,460
amount of time in one half-life 5,730 yrs
8
final mass of the sample half-life
fraction initial mass of the sample
amount of time 1 half-life total time of
decay 1 number of half-lives
12 Math Skills Half-Life
1 8
final mass of the sample
12.5
half-life fraction

initial mass of the sample
100.0

• 1/8 3 half-lives

X
amount of time 1 half-life
total time of decay
21.6

1
number of half-lives
3
21.6 3 7.2 s
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2. 100 1 1/8 3 half-lives 800
8 639,000 y 3 (half-lives) 213,000 y
3. 13 1 1/16 4 half-lives 208
16 60.0 h 4 (half-lives) 15.0 h
10
Half-Life 4. 6.25 1 1/8 3
half-lives 50.0 8 8.10 d x 3
(half-lives) 24.3 days
5. 1/4 2 half-lives 0.025 s x 2
(half-lives) 0.05 s
6. 11.25 1 1/32 5
half-lives 360.00 32 21.6 h x 5 (half-lives)
108.0 h
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• Half-Life
• 62.0 h 12.4 5 (half-lives)
• 5 half-lives 1/32
• 848 g X 1 26.5 g
• 32

8. 1.719 x 104 y 5,730 y 3
(half-lives) 3 half-lives 1/8 144 g X 1
18.0 g 8
9. 2.82 x 109 y 7.04 x 108 y 4.0056 or 4
(half-lives) 4 half-lives 1/16 12.5 g X 16
200 g 1
12
Forces with the Nucleus 1. Attractive nuclear
force between protons 2. Repulsive electric
forces between protons Nuclear force dominates
in all known nuclei. Uranium nuclear force is
just a bit stronger. If a neutron strikes the
nucleus it will split the atom.
This is called fission.
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Fission - is the chemical reaction of several
atoms dividing, splitting and thereby releasing
massive amounts of energy. This large amount of
energy is the result of a chain reaction.
A neutron collides with a nucleus and splits the
atom.
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Fusion - is caused by heating up hydrogen atoms
causing a burst of energy or explosion. They are
fused together. Hydrogen atoms bond together,
releasing large amounts of energy. Like
popcorn getting hot and popping Fusions
potential 8 gallons of sea water 2500
gallons of gas
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2 Protons fuse Hydrogen 2 (deuterium)
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2H proton 3He photon (gamma particle)
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3He 3He 4He 2 protons
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222Rn ------ AX 4He 86 Z
2 ________ decay 210Bi ------ AX 0e
83 Z -1 ________ decay 210Pb ------
210Bi AX 82 83
Z ________ decay
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The half-life of iodine-131 is 8.1 days. The
original sample was 80 g and has decayed to 20 g.
How long did the sample to decay to 20 g? A
sample of strontium-90 is found to have decayed
from a 160 g sample to a 20 g sample after 87.3
years. What is the half-life of
strontium-90? A sample of francium-212 decays
from 64 g to 4 g after 80 minutes. What is the
half-life of francium-212?
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Quiz A Extra Credit Calculate the half-life of
cesium-135 if 7/8 of a sample decays in 6 x
106. Quiz B Extra Credit Calculate the time
required for 3/4 of a sample of cesium-138 to
decay given its half-life is 32.2 minutes.
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Quiz 7 Review
1. Which radiation has no electric charge
associated with it? A. alpha rays B. beta rays C.
gamma rays D. all of these E. none of these
2. The mass of an atomic neutron is nearly A.
twice the mass of an electron. B. four times
the mass of an electron. C. a thousand times
the mass of an electron. D. two thousand times
the mass of an electron.
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4. When a nucleus emits a beta particle, its
atomic number A. remains constant, but its mass
number changes. B. remains constant, and so does
its mass number. C. changes, but its mass number
remains constant. D. changes, and so does its
mass number.
5. A quark is A. an elementary particle. B. a
building block of nucleons. C. a building block
of leptons. D. all of these. E. none of these
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6. An atom with an imbalance of electrons to
protons is A. a lepton B. a beta particle C.
an ion. D. an isotope. E. none of these.
7. The atomic number of an element is the same
as the number of its A. protons B.
neutrons C. nucleons D. neither of these
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8. The atomic mass number of an element is the
same as the number of its A. protons B.
neutrons C. leptons D. none of these
9. Deuterium and tritium are both A. forms of
hydrogen B. isotopes of the same element C.
both of these D. neither of these
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10. Different isotopes of an element have
different numbers of A. protons B.
neutrinos C. photons D. neutrons E. none of
these
11. Electric forces within an atomic nucleus
tend to A. hold it together B. push it
apart C. neither of these
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12. Generally speaking, the larger a nucleus is,
the greater its A. stability B.
instability C. neither stability or instability
13. The half-life of an isotope is one day. At
the end of two days the amount that remains
is A. none B. one-half C. one-quarter D.
one-eighth E. none of these
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14. The half-life on an isotope is one day. At
the end of three days, how much of the isotope
remains? A. none B. one-half C.
one-quarter D. one-eighth E. none of these
17. When an element undergoes nuclear
transmutation, the result is a completely
different A. isotope of the same element B.
ion of the same element C. element
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18. When an alpha particle is ejected from a
nucleus, the nucleus has less A. mass B.
charge C. both of these D. neither of these
19. When a beta particle is ejected from a
nucleus, the nucleus then has a greater A.
mass B. charge C. both of these D. neither
of these
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20. When a gamma ray is emitted by a nucleus,
the nucleus then has appreciably less A.
mass B. charge C. both of these D. neither
of these
21. The fate of the worlds uranium supply is to
eventually become A. alpha and beta
particles B. iron C. lead
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22. The origin of cosmic rays is the A.
Earth B. clouds C. Sun D. cosmos E. none
of these
23. Pure elements can be transformed into
entirely different elements. This statement at
the present time is A. True B. False
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24. Which of the following isotopes is
radioactive? A. carbon-12 B. carbon-14 C.
Both are radioactive D. Neither are radioactive
in nature
25. There is a greater proportion of carbon-14
in A. new bones B. old bones C. same in each
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26. Carbon-14 is produced in the atmosphere
principally by A. plants and animals B.
cosmic ray bombardment C. nitrogen
bombardment D. photosynthesis E. none of these
27. Carbon dating requires that the object being
tested contains A. organic material B.
inorganic material C. charcoal D. sugar
molecules E. none of these
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29. Most of the radioactivity we personally
encounter comes form A. fallout from past and
present testing of nuclear weapons B.
nuclear power plants C. medical X rays D. the
natural environment
30. The amount of radiation we personally
encounter that originates in the Earths and the
atmospheres natural background is A.
a trace amount B. about a quarter C. about
half D. more than half
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31. The source of the Earths natural heat
is A. molten-hot lava B. pressure on the
Earths core C. radioactive decay in the
Earths core D. solar energy in the form of
fossil fuels
32. The most harmful radiations are those
that A. kill living cells B. damage living
cells
33. Radioactivity in the world is something A.
relatively new B. as old as the world itself
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39. When a nucleus emits a beta particle, its
atomic number A. increases by 1 B. decreases
by 1 C. increases by 2 D. decreases by 2 E.
none of these
40. An element will decay to an element with
higher atomic number in the periodic table if it
emits A. a beta particle B. a gamma ray C.
a proton D. an alpha particle E. none of these