Nuclear Physics

Figure 4.7: The Sun

Have you ever wondered what powers the Sun, making it shine so brightly and provide energy to our entire solar system? Or thought about how electricity can be generated from tiny particles inside atoms? At the heart of these incredible phenomena are powerful nuclear reactions that change the very cores—or nuclei— of atoms, releasing immense amounts of energy.

You may be familiar with how Ghana produces electricity from natural resources such as hydropower from rivers, thermal plants burning fuel, solar energy from the sun, and biomass from plants and organic material. These are important and renewable ways to create electricity.

But did you know that electricity can also be produced from inside atoms themselves? This happens through nuclear power, which uses nuclear reactions to release energy stored in the nucleus of atoms. For example, nuclear power plants use a process called nuclear fission, where heavy atoms like uranium are split into smaller parts. This splitting releases huge amounts of heat energy, which is then used to boil water, create steam, and spin turbines that generate electricity.

This method of producing electricity is incredibly efficient because a very small amount of nuclear fuel can generate a large amount of energy, helping to meet the needs of homes, schools, and industries. Nuclear power is an important part of the global energy mix and is used alongside other sources to provide reliable electricity.

In this section, we will explore how nuclear reactions work, how energy is released from atoms, and how humans harness this powerful energy safely to meet our electricity needs—both here on Earth and in the stars above.

Energy from the Atom - E = mc² Nuclear Reactions: Changes within the Core When we talk about “nuclear reactions,” we mean changes happening deep inside the nucleus of an atom. Unlike chemical reactions (where atoms just rearrange), nuclear reactions actually change the types of atoms themselves! These changes can release or absorb huge amounts of energy.

Einstein’s Energy Equation: E=mc² The energy released in nuclear reactions comes from something truly amazing: a tiny bit of mass can be converted directly into energy! This idea was discovered by Albert Einstein and is captured in his world-famous equation:

E=mc² Where:

E = Energy (in Joules, J) m = Mass (in kilograms, kg) c = Speed of light (a very large number: approximately 3×10⁸m/s) Because the speed of light (c) is so large, squaring it (c²) makes it an even bigger number. This means even a tiny bit of mass can turn into an enormous amount of energy!

Mass Defect and Energy Release (The Q-value)

In nuclear reactions, we often find that the total mass of the atoms after the reaction (the products) is slightly less than the total mass of the atoms before the reaction (the reactants). This “missing” mass is called the mass defect. It’s not truly missing; it has been converted into energy! This energy released (or absorbed) in a nuclear reaction is called the Q-value.

Calculating the Q-value

Q = (total mass of reactants−total mass of products) × c²Q = (Δm) c²Where Δm is the mass defect.

· If the products have less mass than the reactants (Δm is positive), energy is released (this is an exothermic reaction).

· If the products have more mass than the reactants (Δm is negative), energy must be supplied for the reaction to happen (this is an endothermic reaction).

Units in Nuclear Physics

In nuclear reactions, masses are often measured in atomic mass units (amu), and energy in megaelectron volts (MeV).

A useful conversion factor: 1 amu = 931.5 MeV /c²This means if you calculate your mass defect in amu, you can multiply it directly by 931.5 MeV to get the energy released.

Fission vs. Fusion - Two Ways to Release Nuclear Energy Two main types of nuclear reactions release energy: fission and fusion.

Nuclear Fission: Splitting Heavy Atoms

What is it?

Nuclear fission is the process where a heavy, unstable atomic nucleus splits into two or more smaller nuclei. When this happens, it releases a significant amount of energy, along with some free neutrons.

How it Works Fission is usually started by firing a neutron at a large, unstable nucleus (like Uranium-235). The neutron is absorbed by the nucleus, making it incredibly unstable. The nucleus then splits apart, releasing energy and more neutrons.

Chain Reaction

The exciting part is that the neutrons released from one fission can then go on to be absorbed by other nearby nuclei, causing them to split. This creates a chain reaction – a self-sustaining process!

· Critical Mass: There’s a minimum amount of fissile material (e.g.

Uranium-235) needed to keep this chain reaction going. This is called the critical mass.

· Control: In nuclear power plants, we use control rods (made of materials like cadmium or boron) to absorb these extra neutrons and keep the chain reaction at a safe, controlled rate.

Where is it used?

1. Nuclear Power Plants: They use controlled fission to generate electricity.

2. Atomic Weapons: These use uncontrolled fission to create massive explosions.

Nuclear Fusion: Combining Light Atoms

What is it?

Nuclear fusion is the process where two or more light atomic nuclei combine to form a heavier nucleus. This process also releases a huge amount of energy, often even more per unit of mass than fission!

How it Works Fusion requires extreme conditions: incredibly high temperatures (millions of degrees Celsius) and immense pressures. These conditions are needed to overcome the natural repulsion between the positively charged nuclei, allowing them to get close enough to “fuse.”

Where does it happen?

· The Cores of Stars: This is how our Sun and all other stars generate their enormous energy! They constantly fuse hydrogen into helium.

· Experimental Fusion Reactors: Scientists are working hard to try and create controlled fusion on Earth, as it promises a clean, virtually limitless energy source.

Examples of Fusion

1. Deuterium (a hydrogen isotope with one proton and one neutron) fuses with Tritium (a hydrogen isotope with one proton and two neutrons) to form Helium, a neutron, and a lot of energy:

2H+³H→⁴He+n+energy

2. Deuterium-Deuterium (D-D) Fusion

2H+²H→³He+n+Energy

3. Proton-Proton Chain (Simplified Overall Reaction, as it’s a multi-step process):

4×¹H→⁴He+2e++2νₑ+Energy Fission vs. Fusion Aspect Nuclear Fission Nuclear Fusion Process Splitting a heavy nucleus into smaller ones Combining light nuclei into a heavier nucleus Natural Occurrence Does not occur naturally (requires initiation) Occurs naturally in stars (e.g., Sun) Energy Released High, but less per unit mass than fusion Very high (3-4 times more than fission per unit mass) Energy Requirement Requires neutron bombardment Requires extremely high temperature and pressure Byproducts Produces long-lived radioactive waste Minimal radioactive waste (mostly stable helium) Applications Nuclear reactors (power), atomic bombs Stars (natural), experimental fusion reactors (future power) Safety Concerns Radioactive waste disposal, meltdown risk Technical challenges in containment, extreme conditions Nuclear Power Generation - The Nuclear Reactor

Figure 4.8: A nuclear reactor assembly

Figure 4.9: Nuclear reactor cooling towers A nuclear reactor is a complex machine designed to control nuclear chain reactions to generate electricity.

How a Nuclear Reactor Works (Simplified)

1. Fuel: Enriched uranium fuel rods (usually Uranium-235) are placed inside the reactor core.

2. Fission: Neutrons are absorbed by the uranium nuclei, causing them to fission and release heat energy. More neutrons are also released.

3. Moderator: A substance like water or graphite surrounds the fuel rods. It slows down the fast neutrons released from fission. These slower neutrons (called “thermal neutrons”) are much better at causing more uranium atoms to split, keeping the chain reaction going efficiently.

4. Control Rods: Rods made of materials that absorb neutrons (like cadmium or boron) can be moved in or out of the core.

a. Insert rods: Slows down the reaction by absorbing more neutrons.

b. Withdraw rods: Speeds up the reaction by absorbing fewer neutrons.

c. These rods control the rate of the chain reaction, preventing it from getting out of control (like in a bomb).

5. Coolant: A fluid (often water) circulates through the reactor core. It absorbs the tremendous heat generated by the fission reactions, preventing the reactor from overheating.

6. Heat Exchange & Steam Generation: The hot coolant then transfers its heat to a separate water loop in a steam generator. This boils water to produce high-pressure steam.

7. Turbine and Generator: The high-pressure steam is directed at a turbine, causing it to spin rapidly. The spinning turbine is connected to an electric generator, which converts this mechanical energy into electrical energy that can be sent to our homes.

8. Containment Structure: The entire reactor system is housed within a massive, strong containment structure (often made of thick concrete and steel). This acts as a final barrier to prevent any radioactive materials from escaping in case of an accident.

Diagrams of a Nuclear Reactor System

Figure 4.10: A nuclear reactor core

Figure 4.11: A Nuclear reactor

Figure 4.12: A Nuclear power plant Hazards and Safety Nuclear power is powerful, but it comes with risks:

1. Radiation Damage: Ionising radiation can harm living cells, causing DNA damage, mutations, cancer, and radiation sickness.

2. Radioactive Waste: Spent nuclear fuel and other materials become radioactive waste, which remains hazardous for thousands of years.

a. Low-level waste: Stored in sealed containers in shallow landfills.

b. High-level waste: Vitrified (turned into glass) and stored deep underground in secure geological repositories.

3. Accident Risk: Although rare, accidents like Chernobyl or Fukushima can release large amounts of radioactive material into the environment.

Figure 4.11: Chernobyl nuclear disaster of 1986 Safety Precautions To manage these risks, strict precautions are taken:

1. Shielding: Using thick barriers of lead, concrete, or water to block radiation.

2. Distance: Keeping a safe distance from radiation sources.

3. Time: Minimising the duration of exposure.

4. Protective Clothing: Workers wear specialised protective gear designed to shield them from hazards.

5. Monitoring: Using devices like dosimeters to track radiation exposure.

6. Strict Regulations: Following international and national guidelines for operation and waste disposal.

Nuclear Stability

Nuclei with higher binding energy per nucleon (abbreviated to BE/A) are more stable because it requires more energy to break them apart. Iron-56 is the most stable nucleus.

Implications for Fission and Fusion

Fusion Very light nuclei (like hydrogen isotopes) have relatively low BE/A. When they fuse to form heavier, more stable nuclei (moving up the BE/A curve towards iron), they release energy because the resulting nucleus has a higher binding energy per nucleon.

Fission Very heavy nuclei (like uranium or plutonium) have lower BE/A compared to medium-sized nuclei. When they split into smaller, more stable nuclei (moving up the BE/A curve towards iron), they release energy because the fission products have a higher binding energy per nucleon than the original heavy nucleus.

Both fission and fusion are processes where the total binding energy of the system increases, leading to the release of energy as the nuclei move towards a state of greater stability.

In summary You have learned that nuclear reactions convert a tiny bit of mass into a huge amount of energy, described by E=mc². This “missing” mass is called the mass defect, and it’s directly related to the binding energy that holds the nucleus together.

The more binding energy per nucleon (protons and neutrons) a nucleus has, the more stable it is!

Key Concepts to Remember

· Nucleons: Protons and neutrons, the particles that make up the nucleus.

· Atomic Number (Z): Number of protons.

· Mass Number (A): Total number of nucleons (protons + neutrons).

· Number of Neutrons (N): A - Z Some formulae

1. Mass Defect (Δm)

Δm = [Z × (mass of a proton) + N × (mass of a neutron)] − (actual mass of the nucleus)

2. Binding Energy (BE)

BE = Δm × c²Or, using the conversion factor for amu to MeV:

BE = Δm (in amu) × 931.5 MeV / amu

3. Binding Energy Per Nucleon (BE/A)

BE / A = Binding Energy_____________ Mass Number (A)

Activity 4.6 Observing, Reflecting, and Discussing the Chernobyl

Disaster Objective: To understand what caused the Chernobyl nuclear disaster, what happened afterward, and what safety lessons were learned.

What you need

1. Access to the following videos

a. The Chernobyl Disaster: How It Happened (Radio Free Europe/ Radio Liberty) (about 13 minutes)

b. Chernobyl Disaster 1986: What Really Happened? (On Demand News) (about 4 minutes)

2. Notebook or paper and pens/pencils for notes and group reflections

3. Quiet space for group viewing and discussion What to do

1. Form small groups Gather where everyone can see and observe the videos clearly, and you have space for discussion.

2. Watch or listen to the First Documentary

a. Play “The Chernobyl Disaster: How It Happened” video.

b. Take notes on key points about what caused the disaster and its immediate effects.

c. Pause at important moments as needed to discuss.

3. Watch the Second Documentary

a. Watch “Chernobyl Disaster 1986: What Really Happened?”

b. Note additional details, especially about the aftermath, health consequences, and long-term impacts on people and the environment.

c. Discuss any new information or perspectives this video provides.

4. Group Reflection and Discussion

Use the following guided questions to facilitate your reflection and discussion:

a. Causes

i. What were the main technical and human factors that caused the accident?

ii. How did the reactor design and safety protocol failures contribute?

b. Consequences

i. What were the immediate impacts on workers and nearby residents?

ii. What long-term effects on health, environment, and society are described?

iii. How large was the evacuation zone and how many people were relocated?

c. Safety Lessons

i. What safety measures and protocols were introduced or improved after the disaster?

ii. Why is radiation dangerous, and what precautions are important to protect people?

iii. What can nuclear power plants do to avoid accidents like Chernobyl in the future?

5. Write a Group Summary

a. Summarise your group’s understanding of

i. The causes of the disaster

ii. Its major consequences

iii. The key safety lessons learned related to radiation hazards and nuclear power safety

b. Prepare to share this summary verbally or in writing with other groups or the class.

Activity 4.7 Comparing Fission and Fusion with Side-by-Side Animations Objective: To help understand the differences between nuclear fission and nuclear fusion by watching animations, comparing what happens in each process, and creating a poster or model to show the steps What you need

1. Devices with internet access to watch the following video animations or access diagrams:

a. Fission Animation: Nuclear fission Atomic energy Animated

b. Fusion Animation: Nuclear fusion - animated 3d program

2. Notebook or worksheet for notes and comparison table

3. Pens or pencils

4. Large paper or poster board (optional, for group summaries)

5. Markers, coloured pencils, large paper/poster board OR modelling clay, cardboard, foam, small balls/beads (for 3D models)

6. Scissors, glue, tape What to do

1. Form Teams: Gather and set up your devices so everyone can see the videos or diagrams.

2. Observe both video animations or review diagrams showing nuclear fission and nuclear fusion processes side by side.

3. Focus on the sequence in each process: What initiates the process, what happens to the nuclei, and what is formed? Pause as needed to take notes or clarify points during viewing.

4. Work together to fill out a FOUR-ROW comparison chart in your notebook or on poster paper:

Comparison Point Fission (What do you observe?)

Fusion (What do you observe?)

Source Nuclei

Products Conditions Required

Energy Output

5. Discuss as a Group: Talk through each point in your chart:

a. Why do the source nuclei differ?

b. Which process needs higher temperatures and why?

c. Why is more energy released in fusion? Where in nature do we find each process?

d. Which of the two processes is considered safer as an electricity generation method? Why?

6. Create a Poster or 3D Model

a. Choose either fission or fusion as your focus.

b. Design a poster (with drawings and labels) OR build a 3D model using craft materials. Your model/poster MUST show:

i. Inputs: The starting materials/nuclei

ii. Process: What happens (splitting or joining)

iii. Outputs: Products formed (new nuclei, neutrons, etc.)

iv. Energy Released: Visualise with arrows, explosion symbols, or labelled light/heat

c. Use colour, labels, and creative touches!

7. Prepare a short explanation answering

a. Which process happens in stars?

b. Which process is used in nuclear reactors on Earth?

c. Point to your model or poster to describe the steps.

Activity 4.8 Exploring Nuclear Reactor Components

Objective: To help understand the main parts of a nuclear reactor and what each part does by using a diagram and matching activity.

What you need

1. Pen or pencil

2. Notebook or paper for notes

3. Labelled diagram of a nuclear reactor showing the key parts (shown below)

Figure 4.11: Diagram of a nuclear reactor What to do

1. Find a partner to work with for this activity.

2. Review the diagram above and discuss.

Take turns explaining each part’s role to your partner, using the diagram for reference.

3. Look at the Parts Table and the Functions Table below. Match each part (from Table 1) to the correct function (from Table 2).

4. Write Your Matches in Your Notebook.

For example, write: Number of the part → [Letter of the matching function] (1 → D)

5. Compare your matches with your partner and talk through any differences or questions.

Table 1: Nuclear Reactor Parts

Part Number Part Name

1 Fuel Rods

2 Moderator 3 Control Rods

4 Coolant

Table 2: Nuclear Reactor Functions

Function Function Description

A Contains the uranium fuel where nuclear fission occurs.

B Absorbs excess neutrons to control or stop the reaction.

C Slows down fast neutrons to make the chain reaction more efficient.

D Removes heat from the reactor core and carries it away.

Activity 4.9 Calculating mass defect and binding energy Study the worked example below carefully before attempting the example questions that follow

Worked example 1

Carbon-12 (¹²C) is a very common and stable isotope, used as the reference for the atomic mass unit.

a. How many protons and neutrons are in a Carbon-12 nucleus?

b. Calculate the

i. expected total mass of its individual nucleons.

ii. mass defect (Δm) for Carbon-12 in amu.

iii. binding energy of the Carbon-12 nucleus in MeV.

iv. binding energy per nucleon for Carbon-12 in MeV/nucleon.

(Atomic Number = 6, mass number = 12, actual atomic mass = 12.000000 amu, mass of proton =1.007276 amu, mass of neutron =1.008665 amu, 1 amu=931.5 MeV/amu)

Solution

a. Number of protons (Z) = 6 Number of neutrons (N) = Mass Number (A) - Atomic Number (Z) = 12−6=6 So, Carbon-12 has 6 protons and 6 neutrons.

b. Expected total mass of individual nucleons = (Z × mp) + (N × mn)

i. Expected mass = (6 × 1.007276 amu) + (6 × 1.008665 amu) Expected mass = 6.043656 amu + 6.051990 amu Expected mass = 12.095646 amu

ii. Mass defect (Δm) = Expected mass − Actual atomic mass Δm = 12.095646 amu − 12.000000 amu Δm = 0.095646 amu

iii. Binding Energy (BE) in MeV = Δm × 931.5 MeV / amu BE = 0.095646 amu × 931.5 MeV / amu BE ≈ 89.07 MeV

iv. Binding Energy per Nucleon (BE / A)in MeV / nucleon = BE_____________ Mass Number (A) BE_ A = 89.07MeV/12 nucleons BE / A ≈ 7.42 MeV / nucleon

Worked example 2

Oxygen-16 (¹⁶O) is the most abundant isotope of oxygen and plays a crucial role in life.

a. How many protons and neutrons are in an Oxygen-16 nucleus?

b. Calculate the

i. expected total mass of its individual nucleons.

ii. mass defect (Δm) for Oxygen-16 in amu.

iii. binding energy of the Oxygen-16 nucleus in MeV.

iv. binding energy per nucleon for Oxygen-16 in MeV/nucleon.

(Atomic Number = 8, mass number = 16, actual atomic mass = 15.994915 amu, mass of proton = 1.007276 amu, mass of neutron = 1.008665 amu, 1 amu = 931.5 MeV/amu)

Solution

a. Protons (Z) and Neutrons (N) Number of protons (Z) = 8 Number of neutrons (N) = Mass Number (A)− Atomic Number (Z) Number of neutrons (N) = 16 − 8 = 8 So, Oxygen − 16 has 8 protons and 8 neutrons.

b. Expected total mass of individual nucleons = (Z×mp)+(N×mn)

i. Expected mass = (8 × 1.007276 amu) + (8 × 1.008665 amu) Expected mass = 8.058208 amu + 8.069320 amu Expected mass = 16.127528 amu

ii. Mass defect (Δm) = Expected mass − Actual atomic mass Δm = 16.127528 amu − 15.994915 amu Δm = 0.132613 amu

iii. Binding Energy (BE) in MeV = Δm × 931.5 MeV / amu BE = 0.132613 amu × 931.5 MeV / amu BE ≈ 123.51 MeV

iv. Binding Energy per Nucleon (BE / A)in MeV / nucleon = BE_____________ Mass Number (A) BE / A = 123.51 MeV/16 nucleons BE / A ≈ 7.72 MeV / nucleon Practice Problems Now, using the worked example as a guide, solve the following problems individually or in groups.

1. Lead-208 (208Pb) is the heaviest known stable isotope and represents a very high point of stability among heavy nuclei.

a. How many protons and neutrons are in a Lead-208 nucleus?

b. Calculate the

i. expected total mass of its individual nucleons.

ii. mass defect for Lead-208 in amu.

iii. binding energy of the Lead-208 nucleus in MeV.

iv. binding energy per nucleon for Lead-208 in MeV/nucleon.

(Atomic Number = 82, mass number = 208, actual atomic mass = 207.976652 amu, mass of proton =1.007276 amu, mass of neutron =1.008665 amu, 1 amu=931.5 MeV/amu)

c. Based on the BE/A values for Carbon-12, Oxygen-16, and Lead-208 (and recalling Iron-56 from your earlier problem), describe the general trend of binding energy per nucleon as the mass number increases, and explain what this trend means for nuclear stability and the possibility of fission or fusion.

Activity 4.10 Role-Play on Radiation Dangers and Waste Handling Objective: To understand the dangers of radiation and how to safely handle radioactive waste by acting out different roles—like a nuclear worker, doctor, or environmental officer What you need

1. Paper or notebook for notes and the worksheet

2. Pens or pencils

3. Optional: simple props like hats, badges, scarves to help with role playing

4. Reference books or internet devices for research

5. Large sheet of paper (optional) to summarise your findings What to do

1. Form small groups of 3-6 people and assign roles within your group (Nuclear Worker(s), Doctor(s), Environmental Officer(s))

2. Research your role: Each person finds out about their role

a. Nuclear Worker: How to recognise radiation hazards, importance of careful waste handling, what protective equipment is used.

b. Doctor: What health risks radiation can cause and how to help people exposed to radiation.

c. Environmental Officer: How radiation affects the environment and how to properly store and monitor radioactive waste.

3. Plan a Short Role-Play (3–5 minutes): Create a small scene where each role explains:

a. What radiation dangers are present

b. What warning signs to look for (like the yellow trefoil symbol)

c. How to handle waste safely

d. What protective equipment to wear and why? Practice your dialogue so everyone knows their part.

4. Perform Your Role-Play

Act out your scene with your group. Be clear and loud enough so everyone listening can understand the dangers and safety steps.

5. Complete the Worksheet

On your worksheet or notebook

a. Draw or list 3 different radiation warning signs you learned about.

b. Draw or name 3 to 4 types of protective equipment (e.g., lead apron, gloves, dosimeter badge).

c. For each, write a short note about what it is and why it is important.

6. Share and Compare

If you can, show your worksheet and role-play with another group. Ask questions and learn new points from their work.

Activity 4.11 Revision of Atomic and Nuclear Physics Areas Objective: To help review and understand key areas in atomic and nuclear physics by working in groups to explain, discuss, and summarise each topic.

What you need

1. Paper or notebooks for writing notes and summaries

2. Coloured pens, markers, or pencils

3. Large sheet(s) of paper, poster board, or digital device (optional) to make a summary poster

4. Textbooks, notes, or internet-enabled devices for research and reference

5. Calculators for calculations

6. Writing tools (pens, pencils, erasers) What to do

1. Form a small group: Sit with your group and organise your materials.

2. Assign each member one or two topics from the list below to focus on

a. Atomic models & energy of a photon

b. Radioactivity & nucleus structure

c. Balancing nuclear reactions

d. Photoelectric effect & wave-particle duality

e. X-rays & nuclear reactions

f. Einstein’s mass-energy relation and its application to nuclear reactors

3. Use your notes, learning material, books, or the internet to

a. Write simple explanations or definitions

b. Write important formulas (e.g., photon energy formula: E = hf)

c. Draw diagrams if you can (like atomic models or nuclear reactions)

d. Give examples or solve small problems if possible

4. Take turns explaining your topic to others in the group. Ask and answer questions about unclear points. Help each other understand key ideas.

5. Together, make a poster or chart that includes

a. Clear bullet points for each topic

b. Diagrams or formulas next to each summary

c. Use colours or headings to divide sections clearly

6. Make and take a quiz

a. Together, write 3 to 5 quiz questions based on all the topics.

b. Take turns asking these questions and answering them as a group.

c. Discuss answers and clarify any misunderstandings.

7. Reflect on your learning

a. Talk about which topics were easiest or hardest.

b. Discuss what helped you understand better.

c. Think about what else you might like to explore more.