Physics 001.002.008 Unstable Radioactive Decay

Alignment

Learning Intentions

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

• Explain why unstable nuclei decay to become more stable.
• Link excess mass to alpha decay.
• Link excess protons to beta positive decay.
• Link excess neutrons to beta negative decay.
• Describe how alpha, beta positive and beta negative decay change the atomic number and mass number of a nuclide.

Success Criteria

By the end of the lesson, students have successfully:

• Identified whether a nucleus is likely to be unstable due to excess mass, excess protons or excess neutrons.
• Explained the type of decay that would reduce the instability.
• Written worded explanations for alpha, beta positive and beta negative decay.
• Used simple nuclear equations to show conservation of mass number and charge number.
• Distinguished between beta positive and beta negative decay in terms of changes inside the nucleus.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 2: Ionising Radiation and Nuclear Reactions
• Nuclear Model and Stability
• Explain how an excess of mass, protons, or neutrons in a nucleus can result in alpha, beta positive and beta negative decay.

Phenomenon

Some nuclei are unstable because their internal arrangement of protons and neutrons is not energetically favourable. For example, very large nuclei such as uranium-238 can reduce their size by emitting an alpha particle. Other nuclei may have too many protons or too many neutrons compared with the stable ratio for their mass. These nuclei can become more stable by changing one type of nucleon into another through beta decay.

A useful guiding question is:

Why do different unstable nuclei emit different types of radiation?

Key Idea

An unstable nucleus decays in a way that moves it toward a more stable combination of mass number, proton number and neutron number.

• A nucleus with excess mass may undergo alpha decay.
• A nucleus with excess protons may undergo beta positive decay.
• A nucleus with excess neutrons may undergo beta negative decay.

Concept

Nuclear stability depends on the balance between the strong nuclear force, electrostatic repulsion between protons, and the neutron-to-proton ratio.

For small stable nuclei, the number of protons and neutrons is often similar. For larger stable nuclei, more neutrons are needed to help stabilise the nucleus because the electrostatic repulsion between many protons becomes stronger.

If a nucleus is unstable, it may decay spontaneously. The decay type depends on the cause of instability.

Alpha Decay: Excess Mass

Alpha decay occurs when a very large nucleus has excess mass and is unstable. The nucleus emits an alpha particle, which is a helium nucleus containing two protons and two neutrons.

General alpha decay equation:

Effects of alpha decay:

• Mass number decreases by .
• Atomic number decreases by .
• The nucleus becomes smaller.
• The neutron number decreases by .
• The proton number decreases by .

Alpha decay is common in very heavy nuclei because it reduces the size of the nucleus and reduces proton-proton repulsion.

Example:

Beta Positive Decay: Excess Protons

Beta positive decay occurs when a nucleus has too many protons compared with neutrons. Inside the nucleus, a proton changes into a neutron and emits a positron.

A positron is the antimatter equivalent of an electron. It has the same mass as an electron but a positive charge.

General beta positive decay equation:

Inside the nucleus:

Effects of beta positive decay:

• Mass number stays the same.
• Atomic number decreases by .
• Proton number decreases by .
• Neutron number increases by .
• The neutron-to-proton ratio increases.

Beta positive decay helps proton-rich nuclei become more stable.

Example:

Beta Negative Decay: Excess Neutrons

Beta negative decay occurs when a nucleus has too many neutrons compared with protons. Inside the nucleus, a neutron changes into a proton and emits an electron.

General beta negative decay equation:

Inside the nucleus:

Effects of beta negative decay:

• Mass number stays the same.
• Atomic number increases by .
• Proton number increases by .
• Neutron number decreases by .
• The neutron-to-proton ratio decreases.

Beta negative decay helps neutron-rich nuclei become more stable.

Example:

Convention

The key conventions associated with the concept and in the branch of established knowledge are below.

Nuclides are written using AZX notation:

where:

• is the chemical symbol.
• is the mass number.
• is the atomic number.

In nuclear equations:

• The total mass number is conserved.
• The total atomic number is conserved.
• Alpha particles are written as .
• Beta positive particles are written as .
• Beta negative particles are written as .

Summary table:

Cause of instability	Decay type	Nuclear change	Effect on	Effect on
Excess mass	Alpha decay	Emits
Excess protons	Beta positive decay		No change
Excess neutrons	Beta negative decay		No change

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.

• Students may think beta particles already exist inside the nucleus before decay. In beta decay, the beta particle is produced during the transformation of a proton or neutron.
• Students may think alpha decay occurs whenever a nucleus has too many neutrons. Alpha decay is more strongly associated with very heavy nuclei that have excess mass.
• Students may confuse beta positive and beta negative decay because both have mass number . The key difference is whether increases or decreases.
• Students may think mass number changes during beta decay. In both beta positive and beta negative decay, stays the same because the total number of nucleons remains constant.
• Students may think radioactive decay happens because atoms “want” to become stable. A better explanation is that unstable nuclei can spontaneously transform into lower-energy, more stable arrangements.

Further Reading

• QCAA Physics Unit 1: Ionising Radiation and Nuclear Reactions
• Nuclear stability and neutron-to-proton ratio
• Alpha, beta positive and beta negative decay equations
• Medical use of beta positive emitters in PET imaging
• Carbon-14 beta negative decay and radiocarbon dating

Explicit Instruction

Begin by revising the meaning of , , protons and neutrons.

For a nuclide written as :

A nucleus is unstable if its arrangement of protons and neutrons has too much energy or an unsuitable neutron-to-proton ratio. Radioactive decay is a spontaneous nuclear process that changes the nucleus into a more stable arrangement.

The type of decay depends on the cause of instability.

1. Excess Mass Leads to Alpha Decay

Very heavy nuclei have many protons and neutrons. The strong nuclear force acts only over very short distances, so it becomes harder to hold a very large nucleus together. At the same time, the many protons repel each other due to electrostatic repulsion.

To reduce its size and become more stable, the nucleus may emit an alpha particle.

Alpha particle:

This contains:

• protons
• neutrons
• mass number
• charge number

General equation:

2. Excess Protons Lead to Beta Positive Decay

A proton-rich nucleus has too many protons compared with neutrons. This increases electrostatic repulsion and gives an unstable neutron-to-proton ratio.

To become more stable, one proton changes into one neutron.

Because the number of protons decreases by , the atomic number decreases by .

General equation:

3. Excess Neutrons Lead to Beta Negative Decay

A neutron-rich nucleus has too many neutrons compared with protons. This also creates an unstable neutron-to-proton ratio.

To become more stable, one neutron changes into one proton.

Because the number of protons increases by , the atomic number increases by .

General equation:

Worked Examples

Worked Example 1

Question:

Uranium-238 undergoes alpha decay. Explain why alpha decay is suitable and write the nuclear equation.

Solution:

Uranium-238 is a very heavy nucleus. It has excess mass and many protons, so electrostatic repulsion is significant. Alpha decay reduces the mass number by and the atomic number by , making the nucleus smaller and more stable.

Original nuclide:

Alpha particle:

Daughter nucleus:

Element with is thorium.

Nuclear equation:

Final explanation:

Uranium-238 undergoes alpha decay because it has excess mass. Emitting an alpha particle reduces both the mass number and proton number, helping the nucleus move toward stability.

Worked Example 2

Question:

Carbon-11 is proton-rich and undergoes beta positive decay. Explain the nuclear change and write the nuclear equation.

Solution:

Carbon-11 has too many protons compared with neutrons. In beta positive decay, a proton changes into a neutron and a positron is emitted.

Inside the nucleus:

Original nuclide:

For beta positive decay:

Element with is boron.

Nuclear equation:

Final explanation:

Carbon-11 undergoes beta positive decay because it has excess protons. The decay decreases the atomic number by and increases the neutron number by , improving the neutron-to-proton ratio.

Worked Example 3

Question:

Carbon-14 is neutron-rich and undergoes beta negative decay. Explain the nuclear change and write the nuclear equation.

Solution:

Carbon-14 has too many neutrons compared with protons. In beta negative decay, a neutron changes into a proton and an electron is emitted.

Inside the nucleus:

Original nuclide:

For beta negative decay:

Element with is nitrogen.

Nuclear equation:

Final explanation:

Carbon-14 undergoes beta negative decay because it has excess neutrons. The decay increases the atomic number by and decreases the neutron number by , improving the neutron-to-proton ratio.

Check for Understanding

Check 1

A nucleus has excess mass and is very large.

Question:

Which type of decay is most likely?

Answer:

Alpha decay.

Reason:

Alpha decay emits , reducing the mass number by and the atomic number by .

Check 2

A nucleus is proton-rich.

Question:

Which type of decay is most likely, and what happens inside the nucleus?

Answer:

Beta positive decay.

Inside the nucleus:

Reason:

A proton changes into a neutron, reducing the atomic number by and improving the neutron-to-proton ratio.

Check 3

A nucleus is neutron-rich.

Question:

Which type of decay is most likely, and what happens to the atomic number?

Answer:

Beta negative decay.

Inside the nucleus:

Reason:

A neutron changes into a proton, so the atomic number increases by .

Investigation (Alternative to Explicit)

Hypothesis

If a nucleus is unstable due to excess mass, excess protons or excess neutrons, then the type of decay can be predicted from the nuclear change that moves the nucleus closer to stability.

Data Collection

Students are given a set of isotope cards. Each card includes:

• nuclide symbol
• mass number
• atomic number
• number of protons
• number of neutrons
• description of instability, such as “very heavy”, “proton-rich” or “neutron-rich”

Example cards:

Nuclide	Description
	Very heavy nucleus
	Proton-rich nucleus
	Neutron-rich nucleus
	Very heavy nucleus
	Proton-rich nucleus
	Neutron-rich nucleus

Students sort each card into one of three decay categories:

• alpha decay
• beta positive decay
• beta negative decay

Analysis

For each isotope, students complete the following table.

Nuclide	Cause of instability	Decay type	Change in	Change in	Daughter nucleus
	Excess mass	Alpha
	Excess protons	Beta positive
	Excess neutrons	Beta negative

Students then write a short explanation for each:

• Why was this decay type suitable?
• How did the proton number change?
• How did the neutron number change?
• How did the decay move the nucleus toward stability?

Evaluation

Students evaluate the model by answering:

• Does the model explain why different nuclei decay in different ways?
• What information is missing if we only know and ?
• Why is the phrase “excess protons” or “excess neutrons” more useful than just saying “unstable”?
• Why is alpha decay more common in very heavy nuclei?

Limitations:

This lesson uses a simplified model of nuclear stability. In reality, nuclear decay depends on nuclear energy levels, binding energy, conservation laws and quantum probability.

Problems

The following problems are designed to help students practise explaining how excess mass, protons or neutrons result in different types of radioactive decay.

1. A radium-226 nucleus undergoes alpha decay.

   a. Explain why alpha decay is suitable for a very heavy nucleus. b. Write the balanced nuclear equation.

   Answer:

2. Sodium-22 is proton-rich and undergoes beta positive decay.

   a. Explain what happens inside the nucleus. b. Write the balanced nuclear equation.

   Answer:

3. Iodine-131 is neutron-rich and undergoes beta negative decay.

   a. Explain what happens inside the nucleus. b. Write the balanced nuclear equation.

   Answer:

4. Complete the table.

Cause of instability	Decay type	Change inside nucleus	Change in	Change in
Excess mass	Alpha	Emits
Excess protons	Beta positive
Excess neutrons	Beta negative

Answers:

Cause of instability	Decay type	Change inside nucleus	Change in	Change in
Excess mass	Alpha	Emits
Excess protons	Beta positive
Excess neutrons	Beta negative

5. A student says, “Beta negative decay happens when a nucleus has too many protons.”

   Explain why this is incorrect.

   Answer:

   Beta negative decay happens when a nucleus has too many neutrons. A neutron changes into a proton and an electron is emitted. This increases the atomic number by and reduces the neutron-to-proton ratio. A nucleus with too many protons would be more likely to undergo beta positive decay.

6. A nucleus changes from to .

   a. Identify the decay type. b. Explain the cause of instability.

   Answer:

   The decay type is beta negative decay because the atomic number increases from to while the mass number stays .

   The original nucleus had excess neutrons. A neutron changed into a proton and emitted a beta negative particle.

7. A nucleus changes from to .

   a. Identify the decay type. b. Explain the cause of instability.

   Answer:

   The decay type is beta positive decay because the atomic number decreases from to while the mass number stays .

   The original nucleus had excess protons. A proton changed into a neutron and emitted a positron.

8. A nucleus changes from to .

   a. Identify the decay type. b. Explain the cause of instability.

   Answer:

   The decay type is alpha decay because the mass number decreases by and the atomic number decreases by .

   The original nucleus had excess mass and was very heavy. It emitted an alpha particle to become smaller and more stable.

Followup

Self-check

Students should be able to answer the following without notes:

• What type of decay is linked to excess mass?
• What type of decay is linked to excess protons?
• What type of decay is linked to excess neutrons?
• In beta positive decay, what happens to a proton?
• In beta negative decay, what happens to a neutron?
• Why does mass number stay the same in beta decay?
• Why does mass number decrease in alpha decay?
• How do alpha, beta positive and beta negative decay help unstable nuclei move toward stability?

Next Topic

The next topic is solving problems involving balancing nuclear equations.

Students will extend this lesson by using conservation of mass number and atomic number to complete nuclear decay equations for alpha, beta positive and beta negative decay.