1. Section 2: Radioactive Decay
Unstable nuclei can break apart spontaneously, changing the identity of atoms. K
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What I Learned

2. 12(B) Describe radioactive decay process in terms of balanced nuclear equations.
2(H) Organize, analyze, evaluate, make inferences, and predict trends from data.
2(I) Communicate valid conclusions supported by the data through methods such as lab reports, labeled drawings, graphs, journals, summaries, oral reports, and technology–based reports.
12(A) Describe the characteristics of alpha, beta, and gamma radiation.
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Radioactive Decay

3. Essential Questions Why are certain nuclei radioactive?
How are nuclear equations balanced?
How can you use radioactive decay rates to analyze samples of radioisotopes?
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Radioactive Decay

4. Vocabulary Review New radioactivity transmutation nucleon
strong nuclear force
band of stability
positron emission
positron
electron capture
radioactive decay series
half-life
radiochemical dating
Radioactive Decay
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5. Nuclear Stability
Except for gamma radiation, radioactive decay involves transmutation, or the conversion of an element into another element.
Protons and neutrons are referred to as nucleons.
All nucleons remain in the dense nucleus because of the strong nuclear force.
The strong nuclear force acts on subatomic particles that are extremely close together and overcomes the electrostatic repulsion among protons.
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Radioactive Decay

6. Nuclear Stability
As atomic number increases, more and more neutrons are needed to produce a strong nuclear force that is sufficient to balance the electrostatic repulsion between protons.
Neutron to proton ratio increases gradually to about 1.5:1.
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Radioactive Decay

7. Nuclear Stability
The area on the graph within which all stable nuclei are found is known as the band of stability.
All radioactive nuclei are found outside the band.
The band ends at Pb-208; all elements with atomic numbers greater than 82 are radioactive.
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Radioactive Decay

8. Types of Radioactive Decay
Atoms can undergo different types of decay—beta decay, alpha decay, positron emission, or electron captures—to gain stability.
In beta decay, radioisotopes above the band of stability have too many neutrons to be stable.
Beta decay decreases the number of neutrons in the nucleus by converting one to a proton and emitting a beta particle.
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Radioactive Decay

9. Types of Radioactive Decay
In alpha decay, nuclei with more than 82 protons are radioactive and decay spontaneously.
Both neutrons and protons must be reduced.
Emitting alpha particles reduces both neutrons and protons.
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Radioactive Decay

10. Types of Radioactive Decay
Nuclei with low neutron to proton ratios have two common decay processes.
A positron is a particle with the same mass as an electron but opposite charge.
Positron emission is a radioactive decay process that involves the emission of a positron from the nucleus.
During positron emission, a proton in the nucleus is converted to a neutron and a positron, and the positron is then emitted.
Electron capture occurs when the nucleus of an atom draws in a surrounding electron and combines with a proton to form a neutron.
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Radioactive Decay

11. Types of Radioactive Decay
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Radioactive Decay

12. Writing and Balancing Nuclear Equations
Nuclear reactions are expressed by balanced nuclear equations.
In balanced nuclear equations, mass numbers and charges are conserved.
Ex. A plutonium-238 atom undergoes alpha decay, write a balanced equation for this decay.
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Radioactive Decay

13. BALANCING A NUCLEAR EQUATION
UNKNOWN
mass number of the product A = ?
atomic number of the product Z = ?
reaction product X = ?
Use with Example Problem 1.
Problem
NASA uses the alpha decay of plutonium-238 ( Pu ) as a heat source on spacecraft. Write a balanced equation for this decay.
SOLVE FOR THE UNKNOWN
Apply the conservation of mass number.
238 = A + 4
Solve for A.
A = = 234
Thus, the mass number of X is 234.
Write the balanced nuclear equation.
The periodic table identifies the element as uranium (U) Pu → U He
Response
ANALYZE THE PROBLEM
You are given that a plutonium atom undergoes alpha decay and forms an unknown product. Plutonium-238 is the initial reactant, while the alpha particle is one of the products of the reaction.
EVALUATE THE ANSWER
The correct formula for an alpha particle is used. The sums of the superscripts and
subscripts on each side of the equation are equal. Therefore, the charge and the
mass number are conserved. The nuclear equation is balanced.
KNOWN
reactant: plutonium-238 ( Pu )
decay type: alpha particle emission ( 2 4 He )
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Radioactive Decay

14. Radioactive Series
A series of nuclear reactions that begins with an unstable nucleus and results in the formation of a stable nucleus is called a radioactive decay series.
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Radioactive Decay

15. Radioactive Decay Rates
A half-life is the time required for one-half of a radioisotope to decay into its products.
Radioactive decay rates are measured in half-lives.
N is the remaining amount.
N0 is the initial amount.
n is the number of half-lives that have passed.
t is the elapsed time and T is the duration of the half-life.
Radioactive Decay
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16. Radioactive Decay Rates
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Radioactive Decay

17. Radioactive Decay Rates
The process of determining the age of an object by measuring the amount of certain isotopes is called radiochemical dating.
Carbon-dating is used to measure the age of artifacts that were once part of a living organism.
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Radioactive Decay

18. CALCULATING THE AMOUNT OF REMAINING ISOTOPE
Use with Example Problem 2.
Problem
Krypton-85 is used in indicator lights of appliances. The half-life of krypton-85 is 11 y. How much of a mg sample remains after 33 y?
Response
ANALYZE THE PROBLEM
You are given a known mass of a radioisotope with a known half-life. You must first determine the number of half-lives that passed during the 33-year period. Then, use
the exponential decay equation to calculate the amount of the sample remaining.
KNOWN
Initial amount = mg
Elapsed time (t) = 33 y Half-life (T ) = 11 y
UNKNOWN
Amount remaining = ? mg
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Radioactive Decay

19. CALCULATING THE AMOUNT OF REMAINING ISOTOPE
SOLVE FOR THE UNKNOWN
Determine the number of half-lives passed during the 33 y.
Number of half-lives (n) = elapsed time (𝑡) half−life(𝑇)
Substitute t = 33 y and T = 11 y.
𝒏= 𝟑𝟑𝒚 𝟏𝟏𝒚 =𝟑.𝟎 𝐡𝐚𝐥𝐟−𝐥𝐢𝐯𝐞𝐬
Write the exponential decay equation.
Amount remaining = (initial amount)( 1 2 )n
Substitute initial amount = mg and n = 3.
Amount remaining = (2.000 mg)( 1 2 )3.0
Amount remaining = (2.000 mg)( 1 8 ) = mg
EVALUATE THE ANSWER
Three half-lives are equivalent to , or The answer (0.25 mg) is equal to of the initial amount. The answer has two significant figures because the number of years has two significant figures. n does not affect the number of significant figures.
Radioactive Decay
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20. Review Essential Questions Vocabulary
Why are certain nuclei radioactive?
How are nuclear equations balanced?
How can you use radioactive decay rates to analyze samples of radioisotopes?
Vocabulary
transmutation
nucleon
strong nuclear force
band of stability
positron emission
positron
electron capture
radioactive decay series
half-life
radiochemical dating
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Radioactive Decay