Physics 001.002.011 Series of Spontaneous Decay

Alignment

Learning Intentions

By the end of the lesson, students will be able to:

• Describe spontaneous radioactive decay as a nuclear process that occurs without an external trigger.
• Represent alpha, beta positive and beta negative decay using nuclear decay equations.
• Identify how the mass number and atomic number change during each type of decay.
• Use conservation of nucleon number and charge to check decay equations.

Success Criteria

By the end of the lesson, students have successfully:

• Written general decay equations for alpha, beta positive and beta negative decay.
• Described the emitted particle in each decay type.
• Predicted the daughter nuclide formed after alpha, beta positive or beta negative decay.
• Checked that the total mass number and atomic number are conserved in a nuclear equation.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 2: Ionising Radiation and Nuclear Reactions
• Describe spontaneous alpha, beta positive and beta negative decay using decay equations.

Phenomenon

Some atomic nuclei are unstable and spontaneously transform into different nuclei. This can happen in naturally occurring radioactive substances such as uranium-238, carbon-14, and potassium-40, or in artificial radionuclides used in medicine such as fluorine-18.

For example, carbon-14 in once-living material spontaneously undergoes beta negative decay. This process allows scientists to estimate the age of archaeological samples through radiocarbon dating.

The key question for this lesson is:

How can we describe spontaneous radioactive decay using nuclear equations?

Key Idea

Concept

Spontaneous radioactive decay occurs when an unstable nucleus changes into a more stable nucleus without being hit by another particle or forced by an external process.

The original nucleus is called the parent nuclide.

The new nucleus formed is called the daughter nuclide.

In a nuclear decay equation:

• the total mass number is conserved
• the total atomic number is conserved
• the emitted radiation shows how the nucleus changed

The three main decay types in this lesson are:

Decay type	Emitted particle	Change in mass number	Change in atomic number
Alpha decay	Alpha particle, or
Beta positive decay	Positron, or	no change
Beta negative decay	Electron, or	no change

Convention

Nuclides are written using notation:

where:

• is the chemical symbol
• is the mass number, equal to the number of protons plus neutrons
• is the atomic number, equal to the number of protons

A decay equation has the form:

Alpha Decay

In alpha decay, the nucleus emits an alpha particle, which is the same as a helium-4 nucleus.

General equation:

$\begin{align}

_Z^AX &\rightarrow _{Z-2}^{A-4}Y + _2

\end{align}$

Example:

Check:

Beta Negative Decay

In beta negative decay, a neutron in the nucleus changes into a proton. An electron and an antineutrino are emitted.

Particle-level equation:

General nuclear equation:

Example:

Check:

Beta Positive Decay

In beta positive decay, a proton in the nucleus changes into a neutron. A positron and a neutrino are emitted.

Particle-level equation:

General nuclear equation:

Example:

Check:

Misconceptions

Common misconceptions students have regarding the concept when applying to various situations and solving problems. It could be a conceptual, mathematical or logical misconception.

• Alpha decay removes only protons. In fact, alpha decay removes two protons and two neutrons.
• Beta particles come from the electron shells. In beta decay, the beta particle is produced by a change inside the nucleus.
• Beta positive and beta negative decay both increase atomic number. In beta negative decay increases by , but in beta positive decay decreases by .
• The mass number changes in beta decay. In beta positive and beta negative decay, the mass number stays the same because the total number of nucleons does not change.
• The daughter element is chosen randomly. The daughter element is determined by the new atomic number .

Further Reading

• QCAA Physics Unit 1: Ionising Radiation and Nuclear Reactions
• Nuclear decay series and radiometric dating
• Medical radioisotopes and positron emission tomography, PET
• Nuclear stability and neutron-to-proton ratio

Explicit Instruction

1. Begin with the idea that spontaneous radioactive decay occurs because some nuclei are unstable.
2. Remind students that the nucleus contains protons and neutrons.
3. Review notation.
4. Explain that nuclear equations must conserve:
   • mass number
   • atomic number
5. Introduce alpha decay:
   • alpha particle is
   • mass number decreases by
   • atomic number decreases by
6. Introduce beta negative decay:
   • neutron changes into proton
   • electron and antineutrino are emitted
   • mass number stays the same
   • atomic number increases by
7. Introduce beta positive decay:
   • proton changes into neutron
   • positron and neutrino are emitted
   • mass number stays the same
   • atomic number decreases by
8. Model how to check both sides of a decay equation.

Worked Examples

Worked Example 1

Question: Describe the alpha decay of radium-226 using a nuclear decay equation.

Step 1: Write the parent nuclide.

Step 2: Alpha decay emits .

Step 3: Find the daughter mass number.

Step 4: Find the daughter atomic number.

Step 5: Identify the element with atomic number .

Atomic number is radon, .

Final answer:

Description: Radium-226 spontaneously emits an alpha particle and forms radon-222.

Worked Example 2

Question: Describe the beta negative decay of carbon-14 using a nuclear decay equation.

Step 1: Write the parent nuclide.

Step 2: Beta negative decay emits an electron and an antineutrino.

Step 3: Mass number does not change.

Step 4: Atomic number increases by .

Step 5: Identify the element with atomic number .

Atomic number is nitrogen, .

Final answer:

Description: Carbon-14 spontaneously emits a beta negative particle and forms nitrogen-14.

Worked Example 3

Question: Describe the beta positive decay of fluorine-18 using a nuclear decay equation.

Step 1: Write the parent nuclide.

Step 2: Beta positive decay emits a positron and a neutrino.

Step 3: Mass number does not change.

Step 4: Atomic number decreases by .

Step 5: Identify the element with atomic number .

Atomic number is oxygen, .

Final answer:

Description: Fluorine-18 spontaneously emits a positron and forms oxygen-18.

Check for Understanding

Check 1

Question: What type of decay is shown below?

Answer: Alpha decay.

Reason: The emitted particle is , which is an alpha particle.

Check 2

Question: Complete the beta negative decay equation.

Answer:

Reason: In beta negative decay, stays the same and increases by .

Check 3

Question: Complete the beta positive decay equation.

Answer:

Reason: In beta positive decay, stays the same and decreases by .

Investigation (Alternative to Explicit)

Hypothesis

If nuclear decay equations conserve mass number and atomic number, then the daughter nuclide formed in alpha, beta positive and beta negative decay can be predicted from the parent nuclide and emitted particle.

Data Collection

Students are given a set of parent nuclides and decay types.

Example data table:

Parent nuclide	Decay type	Emitted particle	Daughter nuclide
	Alpha
	Beta negative
	Beta positive
	Alpha
	Beta negative

Students complete the daughter nuclide column using conservation of and .

Analysis

Students answer:

1. What happens to during alpha decay?
2. What happens to during alpha decay?
3. What happens to during beta negative decay?
4. What happens to during beta negative decay?
5. What happens to during beta positive decay?
6. What happens to during beta positive decay?
7. Why must both sides of a nuclear equation have the same total mass number?
8. Why must both sides of a nuclear equation have the same total atomic number?

Evaluation

Students evaluate their completed equations by checking:

• the total mass number on the left equals the total mass number on the right
• the total atomic number on the left equals the total atomic number on the right
• the daughter element matches the calculated atomic number
• the emitted particle matches the stated decay type

Problems

The following problems are designed to practise describing spontaneous radioactive decay using decay equations.

1. Complete the alpha decay equation:

2. Complete the alpha decay equation:

3. Complete the beta negative decay equation:

4. Complete the beta negative decay equation:

5. Complete the beta positive decay equation:

6. Complete the beta positive decay equation:

7. Identify the type of decay:

8. Identify the type of decay:

9. Identify the type of decay:

10. A student writes the following equation:

Explain why the equation is incorrect and write the correct equation.

Answers

7. Alpha decay.

8. Beta positive decay.

9. Beta negative decay.

10. The equation is incorrect because alpha decay reduces atomic number by , not . The correct equation is:

Followup

Self-check

Students should be able to answer the following without notes:

1. What does spontaneous decay mean?
2. What particle is emitted during alpha decay?
3. What happens to and during alpha decay?
4. What particle is emitted during beta negative decay?
5. What happens to and during beta negative decay?
6. What particle is emitted during beta positive decay?
7. What happens to and during beta positive decay?
8. Why must nuclear equations be balanced?
9. How can the daughter nuclide be identified?
10. What is the difference between beta positive and beta negative decay?

Next Topic

Explain how a radionuclide will, through a series of spontaneous decays, become a stable nuclide.