1. Nuclear Stability and Decay
What determines the type of decay a radioisotope undergoes?
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2. Nuclear Stability and 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.
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3. 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.
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4. 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.
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5. Above atomic number 20, stable nuclei have more neutrons than protons.
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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6. Nuclear Stability and 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. n 1
p + e –1
This process is known as beta emission.
It increases the number of protons while decreasing the number of neutrons.
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7. Nuclear Stability and Decay
Radioisotopes that undergo beta emission include the following. Cu 66 29
Zn + 30 e –1 C 14 6
N + 7 e –1
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8. Nuclear Stability and 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. Co 59 27
Ni e 28 –1 Cl 37 17
Ar e 18 –1
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9. Nuclear Stability and Decay
A positron is a particle with the mass of an electron but a positive charge.
Its symbol is e.
During positron emission, a proton changes to a neutron, just as in electron capture. +1 B 8 5
Be + 4 e +1 O 15 8
N + 7 e +1
the atomic number decreases by 1 and the number of neutrons increases by 1.
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10. Nuclear Stability and 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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11. Nuclear Stability and Decay
In alpha emission, the mass number decreases by four and the atomic number decreases by two. Ra
226 88
Rn He
222 86 4 2 Th
232 90
Ra He
228 88 4 2
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12. Nuclear Stability and 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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13. 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.
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14. 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.
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15. How much of a radioactive sample remains after each half-life?
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16. 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.

17. Half-Life
Decay of 20.0 mg of 15O. What remains after 3 half-lives? After 5 half-lives?

18. Interpret Graphs
A half-life (t ) is the time required for one-half of the nuclei in a radioisotope sample to decay to products. 1 2
After each half-life, half of the original radioactive atoms have decayed into atoms of a new element.
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19. Half-Lives of Some Naturally Occurring Radioisotopes
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
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
Uranium-235
7.0 × 108 years
Uranium-238
4.5 × 109 years
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20. Half-Life
Comparing Half-Lives
Scientists use half-lives of some long-term 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 long-term radiation hazard for patients.
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21. Half-Life
Comparing Half-Lives
Uranium-238 decays through a complex series of unstable isotopes to the stable isotope lead-206.
The age of uranium-containing 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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22. 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
C atoms decay without being replaced.
Archaeologists can use this data to estimate when an organism died. 14 6
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23. 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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24. 1 A = A0  2 Exponential Decay Function n
Half-Life
Exponential Decay Function
A = A0  1 2 n
The exponent n indicates how many times A0 must be multiplied by to determine A. 1 2
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25. Using Half-Lives in Calculations
Sample Problem 25.1
Using Half-Lives in Calculations
Carbon-14 emits beta radiation and decays with a half-life (t ) of 5730 years. Assume that you start with a mass of 2.00 × 10–12 g of carbon-14. 1 2
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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26. Analyze List the knowns and the unknowns.
Sample Problem 25.1
Analyze List the knowns and the unknowns. 1
To calculate the length of three half-lives, multiply the half-life by three.
To find the mass of the radioisotope remaining, multiply the original mass by for each half-life that has elapsed. 1 2
KNOWNS
UNKNOWNS
t = 5730 years
initial mass (A0) = 2.00 × 10–12 g
number of half-lives (n) = 3 1 2
3 half-lives = ? years
mass remaining = ? g
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27. Calculate Solve for the unknowns.
Sample Problem 25.1
Calculate Solve for the unknowns. 2
a. Multiply the half-life of carbon-14 by the total number of half-lives.
t × n = 5730 years × 3 = 17,190 years 1 2
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28. Calculate Solve for the unknowns.
Sample Problem 25.1
Calculate Solve for the unknowns. 2
b. The initial mass of carbon-14 is reduced by one-half for each half-life. So, multiply by three times. 1 2
Remaining mass = 2.00 × 10–12 g × × × 1 2
= × 10–12 g
= 2.50 × 10–13 g
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29. ( ) Calculate Solve for the unknowns. 2
Sample Problem 25.1
Calculate Solve for the unknowns. 2
b. You can get the same answer by using the equation for an exponential decay function.
= (2.00 × 10–12 g)
= × 10–12 g
= 2.50 × 10–13 g
A = A = (2.00 × 10–12 g)
( ) 1 2 n 3 8
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30. The half-life of phosphorus-32 is 14. 3 days
The half-life of phosphorus-32 is 14.3 days. How many milligrams of phosphorus-32 remain after days if you begin with 2.5 mg of the radioisotope?
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31. The half-life of phosphorus-32 is 14. 3 days
The half-life of phosphorus-32 is 14.3 days. How many milligrams of phosphorus-32 remain after days if you begin with 2.5 mg of the radioisotope?
n = days × = 7 half-lives
1 half-life
14.3 days
= (2.5 mg) = 2.0 × 10–2 mg
A = A = (2.5 mg)
( ) 1 2 n 7
( )
128
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32. Which of the following always changes when transmutation occurs?
A. The number of electrons
B. The mass number
C. The atomic number
D. The number of neutrons
C. The atomic number
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33. Key Equation
A = A0  1 2 n
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34. 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