Transcript Document

25.2 Nuclear
Transformations
Nuclear
Stability and >Decay
What determines the type of
decay a radioisotope
undergoes?
1
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Nuclear Stability and
25.2 Nuclear Transformations > Decay
A nucleus may be unstable and undergo
spontaneous decay for different reasons.
The neutron-to-proton ratio in
a radioisotope determines
the type of decay that occurs.
2
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25.2 Nuclear Transformations >
The nuclear force is an attractive
force that acts between all nuclear
particles that are extremely close
together, such as protons and
neutrons in a nucleus.
• At these short distances, the nuclear force
dominates over electromagnetic repulsions and
holds the nucleus together.
3
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25.2 Nuclear
Transformations >
Band
of Stability.
Interpret Data
The stability of a nucleus depends on
the ratio of neutrons to protons.
• This graph
shows the
number of
neutrons vs. the
number of
protons for all
known stable
nuclei.
4
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25.2 Nuclear Transformations >
Interpret Data
• For elements of low
atomic number
(below about 20),
this ratio is about 1.
• Above atomic
number 20, stable
nuclei have more
neutrons than
protons.
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Nuclear Stability and
25.2 Nuclear Transformations > Decay
Some nuclei are unstable because they
have too many neutrons relative to the
number of protons.
• When one of these nuclei decays, a neutron
emits a beta particle (fast-moving electron) from
the nucleus.
– A neutron that emits an electron becomes a proton.
1
0
n
1
1
p
+
0
–1
e
– This process is known as beta emission.
6
– It increases the number of protons while
decreasing the number of neutrons.
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Nuclear Stability and
25.2 Nuclear Transformations > Decay
Radioisotopes that undergo beta emission
include the following.
66
29
7
Cu
66
30
14
6
14
7
C
Zn +
N +
0
–1
0
–1
e
e
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Nuclear Stability and
25.2 Nuclear Transformations > Decay
Other nuclei are unstable because they
have too few neutrons relative to the
number of protons.
• These nuclei increase their stability by
converting a proton to a neutron.
– An electron is captured by the nucleus during this
process, which is called electron capture.
59
28
37
18
8
Ni +
0
–1
Ar +
0
–1
e
59
27
Co
e
37
17
Cl
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Nuclear Stability and
25.2 Nuclear Transformations > Decay
A positron is a particle with the mass of an
electron but a positive charge.
• Its symbol is
0
+1
e.
• During positron emission, a proton changes to a
neutron, just as in electron capture.
8
5
15
8
B
8
4
O
15
7
Be +
N +
0
+1
0
+1
e
e
– the atomic number decreases by 1 and the number
of neutrons increases by 1.
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Nuclear Stability and
25.2 Nuclear Transformations > Decay
Nuclei that have an atomic number
greater than 83 are radioactive.
• These nuclei have both too many neutrons and
too many protons to be stable.
– Therefore, they undergo radioactive decay.
• Most of them emit alpha particles.
– Alpha emission increases the neutron-to-proton
ratio, which tends to increase the stability of the
nucleus.
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Nuclear Stability and
25.2 Nuclear Transformations > Decay
In alpha emission, the mass number
decreases by four and the atomic number
decreases by two.
226
88
232
90
11
Ra
222
86
Th
228
88
Rn +
4
2
He
Ra +
4
2
He
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Nuclear Stability and
25.2 Nuclear Transformations > Decay
Recall that conservation of mass is an
important property of chemical reactions.
• In contrast, mass is not conserved
during nuclear reactions.
• An extremely small quantity of mass
is converted into energy released
during radioactive decay.
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25.2 Nuclear Transformations >
During nuclear decay, if the atomic
number decreases by one but the mass
number is unchanged, the radiation
emitted is
A. a positron.
B. an alpha particle.
C. a beta particle.
D. a proton.
13
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25.2 Nuclear Transformations >
During nuclear decay, if the atomic
number decreases by one but the mass
number is unchanged, the radiation
emitted is
A. a positron.
B. an alpha particle.
C. a beta particle.
D. a proton.
14
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25.2 Nuclear Transformations >
Half-Life
How much of a radioactive
sample remains after each halflife?
15
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Half-Life
Section 15.4 & Screen 15.8
• HALF-LIFE is the time it takes for 1/2 a
sample is disappear.
• The rate of a nuclear transformation
depends only on the “reactant”
concentration.
• Concept of HALF-LIFE is especially useful
for 1st order reactions.
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Half-Life
Decay of 20.0 mg of 15O. What remains after
3 half-lives? After 5 half-lives?
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25.2 Nuclear Transformations >
Interpret Graphs
A half-life (t12) is the time required for onehalf of the nuclei in a radioisotope sample to
decay to products.
After each halflife, half of the
original
radioactive
atoms have
decayed into
atoms of a new
element.
18
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25.2 Nuclear
Transformations >
Comparing
Half-Lives
Half-lives can be as short as a second or
as long as billions of years.
Half-Lives of Some Naturally Occurring Radioisotopes
Isotope
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Half-life
Radiation emitted
Carbon-14
5.73 × 103 years
b
Potassium-40
1.25 × 109 years
b, g
Radon-222
3.8 days
a
Radium-226
1.6 × 103 years
a, g
Thorium-234
24.1 days
b, g
Uranium-235
7.0 × 108 years
a, g
Uranium-238
4.5 × 109 years
a
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25.2 Nuclear Transformations > Half-Life
Comparing Half-Lives
• Scientists use half-lives of some longterm radioisotopes to determine the age
of ancient objects.
• Many artificially produced radioisotopes
have short half-lives, which makes them
useful in nuclear medicine.
– Short-lived isotopes are not a longterm radiation hazard for patients.
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25.2 Nuclear
Transformations > Half-Life
Comparing
Half-Lives
Uranium-238 decays through a complex series of
unstable isotopes to the stable isotope lead-206.
• The age of uraniumcontaining minerals can be
estimated by measuring
the ratio of uranium-238 to
lead-206.
• Because the half-life of
uranium-238 is 4.5 × 109
years, it is possible to use
its half-life to date rocks as
old as the solar system.
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25.2 Nuclear Transformations
> Half-Life
Radiocarbon
Dating
Plants use carbon dioxide to produce
carbon compounds, such as glucose.
• The ratio of carbon-14 to other carbon isotopes
is constant during an organism’s life.
• When an organism dies, it stops exchanging
carbon with the environment and its radioactive
14
6 C atoms decay without being replaced.
• Archaeologists can use this data to estimate
when an organism died.
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25.2 Nuclear Transformations > Half-Life
Exponential Decay Function
You can use the following equation to
calculate how much of an isotope will
remain after a given number of half-lives.
A = A0 
1
2
n
• A stands for the amount remaining.
• A0 stands for the initial amount.
• n stands for the number of half-lives.
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25.2 Nuclear Transformations > Half-Life
Exponential Decay Function
A = A0 
1
2
n
• The exponent n indicates how many times A0
must be multiplied by 12 to determine A.
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25.2 Nuclear Transformations >
Sample Problem 25.1
Using Half-Lives in Calculations
Carbon-14 emits beta radiation and decays with a
half-life (t 12 ) of 5730 years. Assume that you start
with a mass of 2.00 × 10–12 g of carbon-14.
a. How long is three half-lives?
b. How many grams of the
isotope remain at the end of
three half-lives?
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25.2 Nuclear Transformations >
Sample Problem 25.1
1 Analyze List the knowns and the unknowns.
• To calculate the length of three half-lives,
multiply the half-life by three.
• To find the mass of the radioisotope
1
remaining, multiply the original mass by 2 for
each half-life that has elapsed.
KNOWNS
UNKNOWNS
t12 = 5730 years
3 half-lives = ? years
initial mass (A0) = 2.00 × 10–12
g
mass remaining = ? g
number of half-lives (n) = 3
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25.2 Nuclear Transformations >
Sample Problem 25.1
2 Calculate Solve for the unknowns.
a. Multiply the half-life of carbon-14 by
the total number of half-lives.
t 12 × n = 5730 years × 3 = 17,190 years
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25.2 Nuclear Transformations >
Sample Problem 25.1
2 Calculate Solve for the unknowns.
b. The initial mass of carbon-14 is
reduced by one-half for each half-life.
So, multiply by 12 three times.
Remaining mass = 2.00 × 10–12 g × 12 ×12 × 12
= 0.250 × 10–12 g
= 2.50 × 10–13 g
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25.2 Nuclear Transformations >
Sample Problem 25.1
2 Calculate Solve for the unknowns.
b. You can get the same answer by
using the equation for an exponential
decay function.
3
1 n
1
–12 g)
=
(2.00
×
10
2
2
()
A = A0
= (2.00 ×
10–12
()
g)( )
1
8
= 0.250 × 10–12 g
= 2.50 × 10–13 g
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25.2 Nuclear Transformations >
The half-life of phosphorus-32 is
14.3 days. How many milligrams of
phosphorus-32 remain after 100.1
days if you begin with 2.5 mg of the
radioisotope?
30
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25.2 Nuclear Transformations >
The half-life of phosphorus-32 is
14.3 days. How many milligrams of
phosphorus-32 remain after 100.1
days if you begin with 2.5 mg of the
radioisotope?
1 half-life
n = 100.1 days ×
= 7 half-lives
14.3 days
1 n
1 7
2 = (2.5 mg) 2
1
= (2.5 mg) 128
()
A = A0
31
()
( ) = 2.0 × 10
–2
mg
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25.2 Nuclear Transformations >
Which of the following always changes
when transmutation occurs?
A. The number of electrons
B. The mass number
C. The atomic
atomicnumber
number
D. The number of neutrons
32
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25.2 Nuclear Transformations > Key Equation
A = A0 
33
1
2
n
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Kinetics of Radioactive Decay
Activity (A) = Disintegrations/time Activity
(A) = (k)(N)
where N is the number of atoms
Decay is first order, and so
ln (A/Ao) = -kt
The half-life of
radioactive decay is t1/2 = 0.693/k
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