Physics 001.002.005 Nuclide Stability

Alignment

Learning Intentions

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

• Explain nuclide stability in terms of competing nuclear forces.
• Describe how the strong nuclear force acts over very short distances between nucleons.
• Explain why electrostatic repulsion between protons makes nuclei less stable as proton number increases.
• Relate the neutron-to-proton ratio to the stability of light and heavy nuclides.
• Predict whether a nuclide is likely to be stable or unstable from its relative number of protons and neutrons.

Success Criteria

By the end of the lesson, students have successfully:

• Identified that protons repel each other because they have the same positive charge.
• Explained that the strong nuclear force attracts nucleons only over very short distances.
• Explained why neutrons help stabilise a nucleus without adding electrostatic repulsion.
• Compared stable light nuclei, where , with heavier stable nuclei, where .
• Used proton number and neutron number to justify whether a nuclide is likely to be stable.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 2: Ionising Radiation and Nuclear Reactions
• Nuclear Model and Stability
• Explain the stability of a nuclide in terms of the operation of the strong nuclear force over very short distances, electrostatic repulsion, and the relative number of protons and neutrons in the nucleus.

Phenomenon

Some nuclei are stable for billions of years, while others decay almost instantly.

For example:

• Carbon-12, , is stable.
• Carbon-14, , is unstable and undergoes radioactive decay.
• Uranium-238, , is unstable despite having many neutrons.

The key question is:

Why are some combinations of protons and neutrons stable, while others are not?

Key Idea

A nucleus is stable when the attractive strong nuclear force between nucleons is able to overcome the electrostatic repulsion between protons.

Concept

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

A nucleus contains protons and neutrons. These particles are collectively called nucleons.

There are two important interactions inside the nucleus:

1. The strong nuclear force

   • Acts between protons and protons, protons and neutrons, and neutrons and neutrons.
   • Is attractive at normal nuclear distances.
   • Is very strong, but only acts over very short distances.
   • Only significantly affects nucleons that are very close together.

2. Electrostatic repulsion

   • Acts between protons because protons are positively charged.
   • Is repulsive.
   • Acts over longer distances than the strong nuclear force.
   • Increases as the number of protons increases.

A stable nucleus requires the strong nuclear force to hold the nucleus together against proton-proton repulsion.

Neutrons are important because they add attractive strong nuclear force interactions without adding extra electrostatic repulsion.

For light nuclei, stability usually occurs when:

For heavier nuclei, stability usually requires:

where:

• is the number of neutrons
• is the number of protons

Heavier nuclei need proportionally more neutrons because there are more protons repelling each other.

Convention

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

• Proton number is represented by .
• Neutron number is represented by .
• Mass number is represented by .
• The relationship between these is:

• Nuclides are written using notation.
• The neutron number can be found using:

• A nuclide is more likely to be stable if its neutron-to-proton ratio is close to the stable pattern for its size.
• The neutron-to-proton ratio is:

For many light stable nuclei:

For many heavy stable nuclei:

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.

• The strong nuclear force is not the same as gravity. Gravity is far too weak to hold a nucleus together.
• Neutrons are not just “neutral filler”. They help stabilise the nucleus through the strong nuclear force.
• More neutrons does not always mean more stability. Too many neutrons can also make a nucleus unstable.
• The strong nuclear force does not act over large distances. It only operates effectively over very short nuclear distances.
• A large nucleus is not automatically stable just because it has many nucleons. Very large nuclei are often unstable because proton-proton repulsion becomes too large.

Further Reading

• Nuclear model of the atom
• Nuclide notation using
• Electrostatic repulsion between protons
• Strong nuclear force
• Natural radioactive decay
• Alpha, beta positive, beta negative and gamma radiation

Explicit Instruction

The nucleus is a crowded region containing positively charged protons and neutral neutrons.

Since all protons have positive charge, every proton repels every other proton by electrostatic repulsion. If this were the only force acting, the nucleus would fly apart.

However, nuclei can exist because of the strong nuclear force. This force is attractive between nucleons and is much stronger than electrostatic repulsion at very short distances.

The strong nuclear force has a very short range. This means it only strongly attracts nucleons that are very close to each other. A proton on one side of a large nucleus is not strongly attracted to every nucleon on the opposite side, but it can still be repelled by many other protons through electrostatic repulsion.

This explains why larger nuclei need more neutrons. Neutrons increase the number of strong-force attractions without increasing proton-proton repulsion.

For small nuclei, a stable arrangement often has approximately equal numbers of protons and neutrons.

Example:

For carbon-12:

So carbon-12 has 6 protons and 6 neutrons.

Therefore:

This is a stable arrangement for a light nucleus.

For heavier nuclei, stability usually requires more neutrons than protons.

Example:

For lead-208:

Therefore:

Lead-208 is stable even though it has many protons because it has many more neutrons than protons. These neutrons add strong nuclear force attraction without adding electrostatic repulsion.

However, very large nuclei can still be unstable. In very large nuclei, electrostatic repulsion between many protons becomes difficult for the short-range strong nuclear force to overcome. This is why many very heavy nuclides are radioactive; They break down.

Worked Examples

Worked Example 1

Question:

Explain why is stable in terms of protons, neutrons and nuclear forces.

Solution:

Step 1: Identify the number of protons.

So carbon-12 has 6 protons.

Step 2: Calculate the number of neutrons.

Step 3: Compare protons and neutrons.

Carbon-12 has:

So:

Step 4: Explain the stability.

Carbon-12 is a light nuclide with approximately equal numbers of protons and neutrons. The strong nuclear force acts attractively between nearby nucleons and is able to overcome the electrostatic repulsion between the protons.

Final answer:

is stable because it has a suitable balance of protons and neutrons. The strong nuclear force between nearby nucleons is strong enough to overcome the electrostatic repulsion between its 6 protons.

Worked Example 2

Question:

Explain why neutrons help stabilise a nucleus.

Solution:

Protons repel each other because they are all positively charged. This electrostatic repulsion tends to push the nucleus apart.

Neutrons do not have electric charge, so they do not add electrostatic repulsion.

However, neutrons do experience the strong nuclear force. This means neutrons can attract nearby protons and neutrons through the strong nuclear force.

Therefore, neutrons help stabilise a nucleus because they increase attractive strong-force interactions without increasing proton-proton electrostatic repulsion.

Final answer:

Neutrons help stabilise nuclei because they contribute to the attractive strong nuclear force but do not add electrostatic repulsion.

Worked Example 3

Question:

Compare the likely stability of and in terms of nuclear forces.

Solution:

For oxygen-16:

So:

This is suitable for a light nucleus. The strong nuclear force can overcome the electrostatic repulsion between the small number of protons.

For uranium-238:

So uranium-238 has many more neutrons than protons. However, it also has 92 protons. The large number of protons creates significant electrostatic repulsion.

Because the strong nuclear force only acts over very short distances, it cannot fully overcome the repulsion throughout such a large nucleus.

Final answer:

is stable because it is a small nucleus with a balanced number of protons and neutrons. is unstable because its very large number of protons creates strong electrostatic repulsion that cannot be fully overcome by the short-range strong nuclear force.

Check for Understanding

Check 1

Question:

Why do protons in a nucleus repel each other?

Expected answer:

Protons repel each other because they all have positive electric charge. Like charges repel due to electrostatic repulsion.

Check 2

Question:

Why does the strong nuclear force not simply hold every large nucleus together permanently?

Expected answer:

The strong nuclear force is very strong but acts only over very short distances. In large nuclei, not all nucleons strongly attract each other, while protons still experience electrostatic repulsion from many other protons. This makes very large nuclei less stable.

Check 3

Question:

A nuclide has and .

a) Calculate the number of neutrons.

b) Explain whether this neutron-proton balance is reasonable for a light stable nucleus.

Expected answer:

a)

b)

The nuclide has 20 protons and 20 neutrons, so . This is a reasonable balance for a light stable nucleus because the strong nuclear force can overcome the electrostatic repulsion between the protons.

Investigation (Alternative to Explicit)

Hypothesis

A model nucleus will be more stable when attractive interactions between particles are sufficient to overcome repulsive interactions between protons.

Data Collection

Use a classroom model instead of radioactive materials.

Materials:

• Small magnets or magnetic counters
• Two colours of counters, one representing protons and one representing neutrons
• Rubber bands or small Velcro pieces to represent short-range attraction
• A flat tray or whiteboard surface

Method:

1. Use one colour of counter to represent protons.
2. Use another colour of counter to represent neutrons.
3. Build small nuclei with different values of and .
4. Represent proton-proton repulsion by gently spacing proton counters apart.
5. Represent the strong nuclear force by allowing only neighbouring counters to be joined or grouped.
6. Compare small nuclei with to larger nuclei with and larger nuclei with .
7. Record which model nuclei are easiest to keep clustered together.

Suggested data table:

Model nucleus	Number of protons	Number of neutrons	Ratio	Model stability
A	2	2	1.00
B	6	6	1.00
C	12	12	1.00
D	12	18	1.50
E	30	30	1.00
F	30	45	1.50

Analysis

Students should identify patterns:

• Small nuclei can be stable when .
• Larger nuclei require more neutrons to improve stability.
• Adding protons increases electrostatic repulsion.
• Adding neutrons increases strong-force attraction without adding electrostatic repulsion.
• Very large nuclei become difficult to stabilise because the strong nuclear force is short range.

Evaluation

Students should evaluate the model:

• The model is useful because it shows the competition between attraction and repulsion.
• The model is limited because real nuclear forces are not identical to magnets, rubber bands or counters.
• The model does not accurately represent quantum effects or exact nuclear force distances.
• The model helps explain trends in stability but cannot predict exact decay behaviour.

Problems

The following problems are designed to practise explaining nuclide stability using strong nuclear force, electrostatic repulsion and neutron-proton ratio.

1. Calculate the number of neutrons in .

2. Compare and in terms of their proton and neutron numbers.

3. Explain why is less stable than .

4. Calculate the neutron-to-proton ratio for .

5. Calculate the neutron-to-proton ratio for .

6. Calculate the neutron-to-proton ratio for .

7. Explain why heavier stable nuclei usually require more neutrons than protons.

8. Explain why a nucleus containing only protons would be highly unstable.

9. Explain why adding neutrons can improve nuclear stability.

10. Explain why adding too many neutrons can also lead to instability.

11. A nuclide has and . Explain whether this ratio is suitable for a light nucleus.

12. A nuclide has and . Explain why this is unlikely to be stable for a heavy nucleus.

13. A nuclide has and . Calculate and .

14. Explain why electrostatic repulsion becomes more significant as proton number increases.

15. Explain why the strong nuclear force is effective in small nuclei but less able to stabilise very large nuclei.

16. Complete the sentence: A stable nucleus requires a balance between attractive __________ and repulsive __________.

17. True or false: Neutrons increase electrostatic repulsion in the nucleus. Explain your answer.

18. True or false: The strong nuclear force acts over long distances. Explain your answer.

19. Explain why is unstable even though it has more neutrons than protons.

20. Write a paragraph explaining nuclide stability using the terms: protons, neutrons, strong nuclear force, electrostatic repulsion, short range and neutron-to-proton ratio.

Followup

Self-check

Students should be able to answer the following without notes:

• What is the strong nuclear force?
• Why do protons repel each other?
• Why are neutrons important for nuclear stability?
• Why do heavier nuclei need more neutrons than protons?
• Why are many very heavy nuclei unstable?
• How do you calculate neutron number from and ?
• What does the ratio tell us about nuclear stability?

Next Topic

Explain natural radioactive decay in terms of stability.

The next lesson should connect instability to radioactive decay. Students should learn that unstable nuclei can become more stable by emitting radiation, such as alpha, beta positive, beta negative or gamma radiation.