Lesson 28: Radioactive Decay!
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Radioactive decay is a process in which an unstable nucleus undergoes change by emitting radiation. !
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Radiation is a general term for anything that can be radiated out of the nucleus.
Radiation can come in the form of particle (
) or energy (
)
emission. !
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Radioactivity was discovered by accident by Henri Becquerel in 1896. Becquerel
placed a rock containing uranium on a piece of photographic paper inside a dark
drawer. He found that the paper developed an image as if it has been exposed to
a strong light source. !
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Common types of radiation !
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Antimatter:!
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Beta negative
particle
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Beta positive
particle
alpha particle
neutrino
antineutrino
gamma photon
Nuclear Equations!
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Nuclear equations are written like chemical equation, with the original material on one side of the
equation and the resulting material on the other. The two sides are separated by an arrow. !
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Conservation laws and nuclear equations:!
Conservation of nucleons
Conservation of charge
Conservation of antiness
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Example: !
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Common types of radioactive decay!
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Alpha Decay:!
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Example: !
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Beta Negative Decay:!
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Example: !
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Beta Positive Decay:!
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Example: !
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Gamma Radiation:!
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Example: !
The energy released in radioactive decay!
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If you find the total mass of the parent isotopes for a nuclear decay and compare it to the total mass of
the daughter isotopes, there will often be some missing mass. This mass has been converted into
energy, which is released in the kinetic energy of the alpha and beta particles as well as gamma
radiation.!
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Example:!
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Calculate the energy released during the alpha decay of
- Mass of thorium-230 is 230.033134 u!
- Mass of radium-226 is 226.025410 u!
- Mass of alpha particle is 4.002603 u!
230
90
Th
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Radiation Hazards!
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Ionizing radiation consists of particles that have sufficient
energy to knock an electron out of an atom or molecule,
thus forming an ion. A single alpha or beta particle has
enough energy to ionize thousands of molecules.!
Nuclear radiation is potentially harmful to humans because
the ionization it produces can significantly alter the structure
of molecules with in a living cell. !
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Risks of radiation exposure:!
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Type of Radiation
Alpha
Beta
Gamma
Mass
Speed
Penetrating Power
Ionization
Radioactive Decay rates!
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A stable nucleus is one that is much less likely
to undergo radioactive decay. !
In order for a nucleus to be stable, there must
be a balance between the number of protons
and the number of neutrons in the nucleus. !
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Different isotopes decay at different rates.!
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Half life:!
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Example:!
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Uranium-238!
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Uranium-235!
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Carbon-14!
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Decay Curve:!
Formula:!
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Example: Polonium-210 has a half life of 138 days. After 3.8 years, how much of a 765 g sample of
polonium-210 is left?!
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Example: The half-life of a radioactive isotope is 6.8 years. If the activity of the original sample of this
isotope was 4.9 x 105 Bq, what would its activity be after 100 years?!
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Example: You have 75 g of lead at the start of an experiment. How many half lives have passed when
9.3 g remains?!
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Practice Problems:!
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Remember 1 u = 1.660539 x 10 kg!
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1. Write the alpha-decay process for
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-27
234
91
Pa
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2. Which type of beta decay transmutes carbon-14 into nitrogen? Write the process for this decay.!
3. Which type of beta decay transmutes the sodium isotope
decay.!
22
11
Na
into
22
10
Ne
? Write the process for this
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4. Explain whether the atomic number can increase during nuclear decay. Support your answer with
an example. !
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5. What isotope will β decay of thallium-202 produce? Write the process for this decay.!
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6.!
Following are some equations of artificial transmutations produced by particle bombardment.
Using a periodic table, if necessary, determine the other product in each case.!
27
13
a.!
12
6
b.!
9
4
c!.!
1
1
e.!
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7.!
g.!
14
7
d.!
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1
0
14
6
1
0
n → ?
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H
C
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2
1
Na + H → ? +
4
2
N + He → ? +
1
1
1
1
H
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H
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In each of the following equations, determine the emitted particle(s) in each case.!
c.!
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2
1
H +
H
H
1
1
N+ n → ? +
f.!!
b.!
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1
1
C+ H → ? +
23
11
a.!
8.!
2
1
1
1
Be + H → ? +
14
7
d.!
Al + 42 He → ? +
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222
86
238
92
34
17
Rn →
U→
Cl →
218
84
Po + ?
234
90
Th + ?
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e.!
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f.!
35
16
S + ?!
226
222
88 Ra → 86 Rn + ? !
g.!
h.!
141
57
La →
141
58
138
60
Nd →
138
59
212
82
Ce + ?
Pb →
Pr + ?
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212
83
Bi + ? !
215
211
84 Po → 82 Pb + ? !
Radium-226 decays to polonium-214 as follows:!
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226
88
(a)!
Ra →
222
86
(b)!
Rn →
(c)!
218
84
Po →
(d)!
214
82
Pb →
(e)!
214
83
Bi →
214
84
Po !
What kind of particle is emitted in each of the transmutations labeled (a) to (e).!
9. Find the energy in MeV released when alpha decay converts thorium-228 (228.028715 u) into
radium-224 (224.020186 u). The mass of an alpha particle is 4.002603 u.!
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10. Find the quantity of nuclear energy liberated in each of the following nuclear reactions: !
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235
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1
U
n
92
0 !
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(235.043925 u)
(1.00867 u)
3
2
He !
3
—>!
140
54
Xe
94
+!
2 1H ! !
(1.00728 u) !
Sr
38
! +!
!+ !
(139.92161 u) (93.915367 u)!
4
2 He !
2 He !
+!
—>!
(3.01603 u)! (3.01603 u)!
(4.00260 u)!
1
n
20 !
(1.00867 u) !
1
(Answers: 2.96 x 10-11 J, 2.2267 x 10-12 J)!
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11. The half-life of a radioactive isotope is 2.5 years. If the activity of the original sample of this isotope
was 3.2 x 103 Bq, what would be its activity after 5.0 years? [8.0 x 102 Bq]!
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12. What percentage of a polonium-210 sample will remain after 172 days if it has a half-life of 138
days? [42.2%]!
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13. A 2.0 g sample of a radioactive isotope undergoes radioactive decay. If the half-life of this isotope
is 45 mins, how much of this isotope remains after 5.0 hours. [0.020 g]!
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14. In 9.0 days the number of radioactive nuclei decreases to one-eighth the number initially present.
What is the half-life (in days) of the material? [3 days]!
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15. Strontium-82 has a half-life of 25.0 d. If you begin with a sample having a mass of 140 g, in how
many days will you have only 17.5 g of strontium-82 left? [75 days]!
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16. The half-life of a radioactive isotope is 2.5 years. If the activity of the original sample of this isotope
was 3.2 x 103 Bq, what would its activity be after 5.0 years? [8.0 x 102 Bq]!
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