1. Lesson 2
Radioactive Decay

2. Focus Question
Why are some nuclei radioactive?

3. New Vocabulary transmutation positron nucleon electron capture
strong nuclear force
radioactive decay series
band of stability
half-life
positron emission
radiochemical dating

4. Review Vocabulary
radioactivity: the process by which some substances spontaneously emit radiation

5. Nuclear Stability
Except for the emission of gamma radiation, radioactive decay involves transmutation, the conversion of an element into another element.
Whether an atom spontaneously decays and the type of radiation it emits depends on its neutron-to-proton ratio.

6. Nuclear Stability
The protons and neutrons in an atom’s nucleus are referred to as nucleons.
Despite the strong electrostatic repulsion forces among protons, all nucleons remain bound in the dense nucleus because of the strong nuclear force.

7. Nuclear Stability
The strong nuclear force acts on subatomic particles that are extremely close together and overcomes the electrostatic repulsion among protons.

8. Nuclear Stability
Nuclear stability is related to the balance between electrostatic and strong nuclear forces.
The stability of a nucleus can be correlated to its neutron-to-proton (n/p) ratio.

9. Nuclear Stability
For atoms with low atomic numbers (<20), the most stable nuclei are those with neutron-to-proton ratios of 1:1.
As atomic number increases, more neutrons are needed to produce a strong nuclear force sufficient to balance the electrostatic repulsion force between protons.
Therefore, the neutron-to-proton ratio for stable atoms gradually increases, reaching a maximum of approximately 1.5:1.

10. Nuclear Stability
Examine the graph of the number of neutrons versus the number of protons for stable nuclei.
The area on the graph within which all stable nuclei are found is known as the band of stability.

11. Nuclear Stability
The slope of the graph indicates that the number of neutrons required for a nucleus to be stable increases as the number of protons increases.
This correlates with the increase in the neutron-to-proton ratio of stable nuclei with increasing atomic number.

12. Nuclear Stability
All nuclei outside the band of stability—either above or below—are radioactive and undergo decay in order to gain stability. After decay, the new atom is positioned more closely to, if not within, the band of stability.
The band of stability ends at lead-208. All elements with atomic numbers greater than 82 are radioactive.

13. Types of Radioactive Decay
A radioisotope above the band of stability is unstable, as it has too many neutrons relative to its number of protons.
Beta decay decreases the neutron-to-proton ratio by converting a neutron into a proton and emitting a beta particle.

14. Types of Radioactive Decay
Heavy nuclei with more than 82 protons are radioactive and decay spontaneously.
They often undergo alpha decay and emit an alpha particle to reduce the number of neutrons and protons and increase their stability.

15. Types of Radioactive Decay
For nuclei with low neutron-to-proton ratios, two radioactive decay processes occur.
Positron emission is a radioactive decay process that involves the emission of a positron from a nucleus.
A positron is a particle with the same mass as an electron but the opposite charge, represented by β+ or e+.

16. Types of Radioactive Decay
During positron emission, a proton in the nucleus is converted into a neutron and a positron.
The positron is emitted, and the atomic number decreases by one.

17. Types of Radioactive Decay
Electron capture is the other common radioactive-decay process that decreases the number of protons in unstable nuclei below the band of stability.
Electron capture occurs when the nucleus of an atom draws in a surrounding electron, usually one from the lowest energy level.
The captured electron combines with a proton to form a neutron.

18. Types of Radioactive Decay
The atomic number of the nucleus decreases by 1 due to electron capture.
The formation of the neutron also results in an X-ray photon being emitted.

19. Types of Radioactive Decay
Table 3 Summary of Radioactive Decay Processes
Type of Radioactive
Decay
Particle Emitted
Change in Mass Number
Change in Atomic Number
Alpha decay
decreases by 4
decreases by 2
Beta decay
β or e−
no change
increases by 1
Positron emission
β+ or e+
decreases by 1
Electron capture
X-ray photon
Gamma emission γ

20. Writing and Balancing Nuclear Equations
Nuclear reactions are expressed by balanced nuclear equations.
In balanced nuclear equations, mass numbers and charges are conserved.

21. BALANCING A NUCLEAR EQUATION
KNOWN
reactant: plutonium-238 ()
decay type: alpha particle emission ()
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.
UNKNOWN
mass number of the product A = ?
atomic number of the product Z = ?
reaction product X = ?
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.
Apply the conservation of charges.
94 = Z + 2
Solve for Z.
Z = = 92
Thus, the atomic number of X is 92.
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. The reaction is summarized below Pu → 𝒁 𝑨 𝑿 He
You must determine the unknown product of the reaction.

22. BALANCING A NUCLEAR EQUATION
SOLVE FOR THE UNKNOWN continued
Write the balanced nuclear equation.
The periodic table identifies the element as uranium (U) Pu → U He
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.

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

24. Radioactive Decay Rates
Radioactive decay rates are measured in half-lives.
A half-life is the time required for one-half of a radioisotope’s nuclei to decay into its products.

25. Radioactive Decay Rates
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.

26. Radioactive Decay Rates

27. Radioactive Decay Rates

28. 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

29. CALCULATING THE AMOUNT OF REMAINING ISOTOPE
SOLVE FOR THE UNKNOWN
Determine the number of half-lives.
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 = 3.0
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.

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

31. Quiz 1.
What determines whether an atom spontaneously decays and the type of radiation it emits?
whether it has nucleons A
whether it is influenced by the strong nuclear force B
its neutron-to-proton ratio C
CORRECT
none of the above D

32. Quiz 2.
What is the name of the area on a graph of the number of neutrons versus the number of protons within which all stable nuclei are found?
band of stability A
CORRECT
neutron-to-proton ratio B
slope ratio C
radioactive decay series D

33. Quiz 3.
Which of the following is true of nuclei outside the band of stability?
They are radioactive. A
CORRECT
They all have neutron-to-proton ratios of 1:1. B
They all undergo beta decay. C
They cannot undergo decay to gain stability. D

34. Quiz 4.
A radioactive decay series is a series of nuclear reactions that begins with a(n) _______ nucleus and results in the formation of a(n) _______ nucleus.
uranium; plutonium A
stable; unstable C
carbon; nitrogen B
unstable; stable D
CORRECT

35. Quiz 5. How are radioactive decay rates measured?
as neutron-to-proton ratios A
in half-lives B
CORRECT
by atomic number C
Radioactive decay rates cannot be measured. D