Physics 001.002.003 Proton Repulsion

Physics 001.002.003 Repulsion

Alignment

Learning Intentions

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

• Explain why protons in the nucleus repel each other.
• Describe electrostatic repulsion between like charges.
• Connect proton-proton repulsion to the need for another force inside the nucleus.
• Use Coulomb’s law qualitatively to explain why repulsion becomes significant at very small distances.

Success Criteria

By the end of the lesson, students have successfully:

• Stated that protons are positively charged and therefore repel other protons.
• Explained that the electrostatic force acts between charged particles.
• Identified that like charges repel and opposite charges attract.
• Described that proton-proton repulsion becomes very large because protons in the nucleus are extremely close together.
• Recognised that the nucleus requires the strong nuclear force to remain stable.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics
• Topic 2: Ionising Radiation and Nuclear Reactions
• Nuclear Model and Stability
• Explain why protons in the nucleus repel each other.

Phenomenon

A helium nucleus contains two protons packed into an extremely small region of space. Since both protons are positively charged, they should repel each other strongly. Yet, many nuclei remain stable. This raises the question:

Why do protons in the nucleus repel each other, and why does the nucleus not immediately fly apart?

Key Idea

Protons repel each other because they both have positive electric charge. This repulsion is an electrostatic force. There is another force that brings them together called the strong nuclear force; The strong nuclear force does not yet conform to our current understanding, but it can be modelled.

Concept

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

Protons have positive electric charge. According to the electrostatic interaction, particles with the same type of charge repel each other. Since every proton has charge , any two protons in a nucleus exert a repulsive force on each other.

This can be represented using Coulomb’s law:

For two protons:

Since both charges are positive, the interaction is repulsive. Also, because the distance between protons in the nucleus is extremely small, the value of becomes very large.

Convention

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

• Protons have charge .
• Electrons have charge .
• Neutrons have no net electric charge.
• Like charges repel.
• Opposite charges attract.
• Electrostatic force acts over distance between charged particles.
• The direction of the electrostatic force on a proton due to another proton is away from the other proton.
• Coulomb’s law shows that electrostatic force increases as separation distance decreases in inverse square relationship.

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.

• Protons repel because they are “moving fast” inside the nucleus.
• Neutrons cancel out the positive charge of protons.
• The nucleus is stable because electrostatic repulsion disappears at small distances.
• Protons only repel outside the nucleus, not inside it.
• A larger nucleus is always more stable because it has more particles.

Further Reading

• Review electric charge and electrostatic forces.
• Preview the strong nuclear force.
• Preview nuclear stability and neutron-proton ratio.

Explicit Instruction

The nucleus contains protons and neutrons. Protons are positively charged, while neutrons have no net electric charge. Because protons are all positively charged, each proton repels every other proton in the nucleus.

This repulsion is caused by the electrostatic force. The rule for electric charge is:

• like charges repel
• opposite charges attract

Therefore:

and repel

and attract

and repel

Inside the nucleus, protons are separated by distances of about . This is an extremely small distance. Coulomb’s law shows that the electrostatic force depends on the inverse square of the distance:

This means that as becomes smaller, becomes much larger. Therefore, because protons in the nucleus are very close together, the repulsive electrostatic force between them is very strong.

However, nuclei do not always fall apart. This tells us that another attractive force must act inside the nucleus. This force is called the strong nuclear force. It acts over very short distances and can overcome electrostatic repulsion in stable nuclei.

Worked Examples

Worked Example 1

Question:

Why do two protons repel each other?

Solution:

A proton has positive electric charge. Another proton also has positive electric charge. Since like charges repel, the two protons exert repulsive electrostatic forces on each other.

Therefore, two protons repel because they both have positive charge.

Worked Example 2

Question:

Explain why the repulsion between protons inside the nucleus is large.

Solution:

The electrostatic force between two charged particles is described by:

For two protons:

The charges are the same sign, so the force is repulsive.

The distance between protons in the nucleus is extremely small. Since is in the denominator and is squared, a very small produces a very large force.

Therefore, proton-proton repulsion in the nucleus is large because the protons are extremely close together.

Worked Example 3

Question:

A nucleus contains 6 protons. Explain why there is more electrostatic repulsion in this nucleus than in a helium nucleus with 2 protons.

Solution:

Each proton repels every other proton. A helium nucleus has 2 protons, so there is only one proton-proton repulsion pair.

A nucleus with 6 protons has many more proton-proton pairs. Since each pair produces electrostatic repulsion, the total repulsion inside the nucleus is greater.

Therefore, nuclei with more protons generally experience greater total electrostatic repulsion.

Check for Understanding

Check 1

Question:

What charge does a proton have?

Expected answer:

A proton has positive charge, .

Check 2

Question:

Why do protons repel each other?

Expected answer:

Protons repel because they have the same positive electric charge, and like charges repel.

Check 3

Question:

Why is proton-proton repulsion especially important inside the nucleus?

Expected answer:

Protons inside the nucleus are extremely close together. Since electrostatic force increases as distance decreases, the repulsion between protons becomes very large.

Investigation (Alternative to Explicit)

Hypothesis

If two objects have the same type of electric charge, then they will repel each other because like charges repel.

Data Collection

Students can investigate electrostatic repulsion using simple classroom materials:

• two balloons
• wool cloth or hair
• string
• retort stand or support

Method:

1. Inflate two balloons and tie each to a string.
2. Rub both balloons with wool or hair.
3. Suspend the balloons close together.
4. Observe the motion of the balloons.
5. Record whether the balloons attract, repel, or show no clear interaction.

Analysis

Students should identify that rubbing the balloons transfers charge. When both balloons receive the same type of charge, they repel each other.

This models the idea that like charges repel. In the nucleus, protons are all positively charged, so they also repel each other.

The balloon model is not a nuclear model because balloons are macroscopic objects and the nucleus involves subatomic particles. However, the model is useful for representing the rule that like charges repel.

Evaluation

Limitations:

• Balloons are much larger than protons.
• Balloon charge is produced by electron transfer, not by changing the identity of particles.
• The model shows electrostatic repulsion but does not show the strong nuclear force.
• The model does not show the extremely small distances inside the nucleus.

Improvements:

• Repeat the demonstration several times.
• Control how long each balloon is rubbed.
• Compare charged balloons with uncharged balloons.
• Use diagrams to connect the model to proton-proton repulsion in a nucleus.

Problems

The following problems are designed to practise explaining proton-proton repulsion.

1. State the charge of a proton.

2. State the rule for the interaction between like charges.

3. Explain why two protons repel each other.

4. A nucleus contains 3 protons. Explain why each proton experiences electrostatic repulsion.

5. Use Coulomb’s law qualitatively to explain why proton-proton repulsion becomes stronger when protons are closer together.

6. Explain why a nucleus with more protons generally has more electrostatic repulsion.

7. Complete the sentence: Protons repel each other because they are both __________ charged.

8. A student says, “Neutrons stop protons from being positively charged.” Explain why this is incorrect.

9. A student says, “Protons only repel if they are outside the nucleus.” Explain why this is incorrect.

10. Explain why the existence of stable nuclei suggests that another force must act inside the nucleus.

Followup

Self-check

Students should be able to answer the following:

• Can I state the charge of a proton?
• Can I explain why like charges repel?
• Can I explain why two protons repel?
• Can I connect proton-proton repulsion to Coulomb’s law?
• Can I explain why the nucleus needs another force to remain stable?

Next Topic

The next topic is:

Describe the concept of the strong nuclear force.

This follows naturally because proton-proton electrostatic repulsion should push the nucleus apart, yet many nuclei are stable. The strong nuclear force explains how protons and neutrons can remain bound together in the nucleus.