Physics 001.002.006 Natural Radioactive Decay

Alignment

Learning Intentions

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

• Explain natural radioactive decay as a process that occurs when an unstable nucleus changes to become more stable.
• Link nuclear stability to the balance between the strong nuclear force, electrostatic repulsion, and the neutron-to-proton ratio.
• Describe how alpha, beta and gamma decay can move an unstable nucleus toward a more stable arrangement.
• Interpret simple nuclear stability situations using proton number, neutron number and mass number.

Success Criteria

By the end of the lesson, students have successfully:

• Identified whether a nucleus is likely to be stable or unstable based on size and neutron-to-proton balance.
• Explained that radioactive decay is spontaneous because unstable nuclei can move to a lower-energy, more stable state.
• Matched alpha, beta negative, beta positive and gamma decay to the type of instability they can reduce.
• Used nuclear notation to describe how the nucleus changes during radioactive decay.

Syllabus Reference

• QCAA Physics Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 2: Ionising Radiation and Nuclear Reactions
• Science Understanding: Nuclear Model and Stability
• Subject matter: Explain natural radioactive decay in terms of stability.

Phenomenon

Some rocks, minerals and even living things contain naturally occurring unstable nuclei. For example, carbon-14 is produced naturally in the atmosphere and is found in living organisms. Uranium-238 occurs naturally in rocks. These nuclei are not stable forever. Without being heated, pushed, struck or chemically changed, they can spontaneously emit radiation and transform into different nuclei.

The key question is:

Why does a nucleus decay naturally if nothing appears to trigger it?

Key Idea

Natural radioactive decay occurs because some nuclei are unstable. An unstable nucleus can spontaneously change into a more stable nucleus by emitting radiation. The decay process moves the nucleus toward a lower-energy, more stable arrangement of protons and neutrons.

Concept

The concept and thought that best describes the cause of the phenomenon is below.

A nucleus is stable when the forces inside it are balanced well enough for it to remain unchanged over time. Three important factors affect nuclear stability:

1. Strong nuclear force

   • Acts between nucleons, meaning protons and neutrons.
   • Is attractive.
   • Is very strong, but only over extremely short distances.
   • Helps hold the nucleus together.

2. Electrostatic repulsion

   • Acts between protons because they are positively charged.
   • Protons repel other protons.
   • Repulsion becomes more significant as the number of protons increases.

3. Relative number of neutrons and protons

   • Neutrons add strong nuclear attraction without adding electrostatic repulsion.
   • Small stable nuclei often have similar numbers of protons and neutrons.
   • Larger stable nuclei usually require more neutrons than protons.
   • If a nucleus has too many neutrons, too many protons, or is too massive, it may be unstable.

A nucleus undergoes natural radioactive decay when it can become more stable by changing its composition or energy.

Radioactive decay is:

• spontaneous: it occurs without an external trigger.
• random for an individual nucleus: we cannot predict exactly when one nucleus will decay.
• predictable for a large sample: patterns emerge when many nuclei are present.
• a nuclear process: it changes the nucleus, not the electron arrangement.

Convention

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

Nuclides are written using nuclear notation:

where:

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

The number of neutrons is:

In radioactive decay, the parent nucleus changes into a daughter nucleus:

The daughter nucleus is usually more stable than the parent nucleus.

Common decay types can be connected to different types of instability:

Type of instability	Possible decay process	Stability effect
Nucleus is very large and has too much mass	Alpha decay	Reduces mass number and proton number
Nucleus has too many neutrons	Beta negative decay	Converts a neutron into a proton
Nucleus has too many protons	Beta positive decay	Converts a proton into a neutron
Nucleus has excess energy after another decay	Gamma decay	Releases energy without changing proton or neutron number

Alpha decay:

Beta negative decay:

Beta positive decay:

Gamma decay:

The star means the nucleus is in an excited, higher-energy state.

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.

• Radioactive decay happens because the atom is old.
• Radioactive decay happens because the atom is heated or exposed to light.
• A radioactive atom always becomes completely safe after one decay.
• Gamma decay changes the number of protons or neutrons.
• Beta radiation comes from the electron shells rather than the nucleus.

Further Reading

• QCAA Physics Unit 1: Ionising Radiation and Nuclear Reactions
• Nuclide chart or table of stable isotopes
• Simulations showing random decay and half-life
• Background radiation and naturally occurring radioisotopes in rocks, soil and the atmosphere

Explicit Instruction

Natural radioactive decay is best explained as a stability problem.

A nucleus contains protons and neutrons. Protons repel each other because they are all positively charged. The strong nuclear force attracts nucleons together, but it only works over very short distances. In small nuclei, this attractive force can usually overcome proton-proton repulsion if the neutron-to-proton ratio is suitable.

As nuclei become larger, proton-proton repulsion becomes harder to overcome. More neutrons are needed to help stabilise the nucleus because neutrons contribute to the strong nuclear force without adding electrostatic repulsion. However, too many neutrons also creates instability.

Therefore, unstable nuclei decay naturally because the current arrangement of protons and neutrons is not the most stable possible arrangement.

Radioactive decay is the process by which an unstable parent nucleus emits radiation and forms a more stable daughter nucleus.

The type of decay depends on the type of instability.

If the nucleus is very large, alpha decay can make it more stable by reducing both mass number and proton number.

Example:

Uranium-238 is very large. By emitting an alpha particle, it decreases its mass number from to and its atomic number from to . This reduces the size of the nucleus and reduces electrostatic repulsion.

If the nucleus has too many neutrons, beta negative decay can make it more stable by changing a neutron into a proton.

Example:

Carbon-14 has too many neutrons to be stable. Beta negative decay increases the atomic number from to while the mass number remains .

If the nucleus has too many protons, beta positive decay can make it more stable by changing a proton into a neutron.

Example:

The mass number remains , but the atomic number decreases from to .

If the nucleus has excess energy, gamma decay can make it more stable by releasing energy.

Example:

The mass number and atomic number do not change. The nucleus simply moves from a higher-energy state to a lower-energy state.

Worked Examples

Worked Example 1

A uranium-238 nucleus undergoes alpha decay.

Explain why alpha decay can increase nuclear stability.

Given:

Alpha decay emits:

The daughter nucleus has:

Therefore:

Explanation:

Uranium-238 is a very large nucleus. It contains many protons, so electrostatic repulsion is large. Alpha decay reduces the number of protons and the total number of nucleons. This can move the nucleus toward a more stable arrangement.

Worked Example 2

Carbon-14 undergoes beta negative decay.

Explain why beta negative decay is suitable for a neutron-rich nucleus.

Carbon-14 has:

Carbon-14 has protons and neutrons. It is neutron-rich compared with stable carbon-12, which has protons and neutrons.

In beta negative decay, a neutron changes into a proton and an electron is emitted.

The mass number stays the same, but the atomic number increases.

Explanation:

Beta negative decay reduces the neutron-to-proton ratio by decreasing the number of neutrons and increasing the number of protons. This can make a neutron-rich nucleus more stable.

Worked Example 3

An excited nickel-60 nucleus emits gamma radiation.

Explain why gamma decay does not produce a different element.

Gamma decay is:

Before decay:

After decay:

The number of protons has not changed, so the element is still nickel.

Explanation:

Gamma decay releases excess energy from the nucleus. It does not change the number of protons or neutrons. The nucleus becomes more stable because it moves to a lower-energy state.

Check for Understanding

Check 1

A nucleus has a very large number of protons and neutrons. Which type of decay is likely to help reduce its size?

Expected answer:

Alpha decay, because it emits a helium nucleus and reduces both mass number and atomic number.

Check 2

A nucleus has too many neutrons compared with stable nuclei of similar size. Which decay process can reduce the neutron-to-proton ratio?

Expected answer:

Beta negative decay, because a neutron changes into a proton and an electron is emitted.

Check 3

A nucleus emits gamma radiation. Has it become a different element?

Expected answer:

No. Gamma decay releases energy from the nucleus but does not change the number of protons. Since the atomic number stays the same, the element stays the same.

Investigation (Alternative to Explicit)

Hypothesis

If a model nucleus has an unbalanced neutron-to-proton ratio or is too large, then it will be classified as unstable and matched with a decay type that moves it toward greater stability.

Data Collection

Students are given nuclide cards showing:

• nuclide notation
• number of protons
• number of neutrons
• whether the nucleus is small, medium or large
• position relative to the band of stability

Example cards:

Nuclide	Protons	Neutrons	Stability issue
			Very large nucleus
			Too many neutrons
			Too many protons
			Excess nuclear energy

Students sort each card into one of the following categories:

• likely alpha decay
• likely beta negative decay
• likely beta positive decay
• likely gamma decay
• likely stable

Analysis

Students explain their sorting using the following prompts:

1. What makes the nucleus unstable?
2. Which decay type would move the nucleus toward stability?
3. What changes happen to , and ?
4. Does the decay create a new element?

Evaluation

Students evaluate limitations of the card-sort model:

• It simplifies the band of stability.
• It does not show exact nuclear binding energies.
• It suggests decay type can always be predicted easily, but real decay pathways may be more complex.
• It does not show probability or half-life.
• It does not show that some radionuclides decay through a series of steps before becoming stable.

Problems

The following problems are designed to practise explaining radioactive decay in terms of nuclear stability.

1. Explain why a nucleus with many protons may be unstable.

2. Explain why neutrons can help stabilise a nucleus.

3. A nucleus has too many neutrons. a. Which decay type is likely? b. What happens to the atomic number? c. What happens to the mass number?

4. A nucleus has too many protons. a. Which decay type is likely? b. What happens to the atomic number? c. What happens to the mass number?

5. Complete the alpha decay equation:

6. Complete the beta negative decay equation:

7. Complete the gamma decay equation:

8. Explain why gamma decay can make a nucleus more stable even though it does not change the number of protons or neutrons.

9. A student says, “Radioactive decay happens because the atom wants to get rid of electrons.” Explain why this statement is incorrect.

10. A parent nucleus decays into a daughter nucleus, but the daughter nucleus is still unstable. Explain what may happen next.

Followup

Self-check

Students should be able to answer the following questions:

• Can I explain why some nuclei are unstable?
• Can I describe the roles of the strong nuclear force and electrostatic repulsion?
• Can I explain why larger nuclei need more neutrons?
• Can I link alpha decay to large unstable nuclei?
• Can I link beta negative decay to neutron-rich nuclei?
• Can I link beta positive decay to proton-rich nuclei?
• Can I explain why gamma decay lowers nuclear energy without changing the element?
• Can I explain why radioactive decay is spontaneous and natural?

Next Topic

The next topic is:

Describe alpha, beta positive, beta negative and gamma radiation, including the properties of penetrating ability, charge, mass and ionisation ability.

This lesson will extend the idea of nuclear stability by comparing the radiation emitted during different decay processes.