Grade 12

Advanced

10 min

Lesson 10 of 12

Nuclear Fission and Fusion

Not Started

Investigating the large-scale release of energy through splitting heavy nuclei or fusing light ones.

How can a single gram of Uranium-235 produce as much energy as burning three tons of coal? The answer lies in the 'mass defect'—a tiny amount of matter vanishing to release the most concentrated energy in the universe.

Learning Objectives

1.Explain the mechanisms of induced nuclear fission and the conditions for self-sustaining chain reactions.
2.Analyze the extreme temperature and pressure requirements for nuclear fusion in stellar cores.
3.Compare the energy density and environmental impacts of fission-based power versus potential fusion reactors.

Induced Fission and the Binding Energy Curve

Nuclear fission occurs when a heavy nucleus, such as

^{235}_{92}U

, becomes unstable and splits into two smaller 'daughter' nuclei. This is typically induced by capturing a slow-moving 'thermal' neutron. According to the Binding Energy per Nucleon curve, heavy nuclei are less stable than medium-sized ones. When a heavy nucleus splits, the resulting fragments have a higher binding energy per nucleon, meaning they are in a more stable, lower-energy state. The 'missing' mass, known as the mass defect (

\Delta m

), is converted into kinetic energy and gamma radiation following Einstein’s mass-energy equivalence:

E = \Delta m c^2

Quick Check

Why does the fission of a heavy nucleus release energy rather than requiring it?

Think about the stability of the products versus the reactants on the binding energy curve.

Answer

Because the daughter nuclei have a higher binding energy per nucleon than the parent nucleus, resulting in a net loss of mass that is converted into energy.

Chain Reactions and Criticality

A single fission event of $^{235}U$ releases an average of 2.5 neutrons. If these neutrons go on to induce further fission in neighboring nuclei, a chain reaction occurs. To maintain a steady power output in a nuclear reactor, the reaction must reach criticality, where exactly one neutron from each fission event triggers another. This is managed using moderators (like water or graphite) to slow down fast neutrons and control rods (like boron or cadmium) to absorb excess neutrons. If the reaction becomes 'supercritical' without control, an exponential release of energy occurs, which is the principle behind nuclear weapons.

Calculate the energy released from a single fission event where the mass defect is $\Delta m = 3.2 \times 10^{-28}$ kg.

1. Identify the formula: $E = \Delta m c^2$ . 2. Use the speed of light $c \approx 3.0 \times 10^8$ m/s. 3. Substitute values: $E = (3.2 \times 10^{-28} \text{ kg}) \times (3.0 \times 10^8 \text{ m/s})^2$ . 4. Calculate: $E = 2.88 \times 10^{-11}$ Joules. 5. Convert to MeV (if required) using $1 \text{ MeV} = 1.6 \times 10^{-13}$ J: $E \approx 180 \text{ MeV}$ .

Nuclear Fusion: The Stellar Engine

Nuclear fusion is the process of combining light nuclei, such as Hydrogen isotopes, to form a heavier nucleus like Helium. This process powers stars. However, nuclei are positively charged and strongly repel each other via the Coulomb force. To overcome this 'Coulomb barrier' and allow the Strong Nuclear Force to take over, nuclei must be moving at incredible speeds. This requires temperatures in the millions of degrees (plasma state) and high pressures to increase the collision frequency. In the Sun, the proton-proton chain dominates, while experimental reactors on Earth focus on the Deuterium-Tritium (

D-T

) reaction:

^2_1H + ^3_1H \rightarrow ^4_2He + ^1_0n + 17.6 \text{ MeV}

Compare the energy per nucleon for Fission ( $200 \text{ MeV}$ for 236 nucleons) vs Fusion ( $17.6 \text{ MeV}$ for 5 nucleons).

1. Fission: $\frac{200}{236} \approx 0.85 \text{ MeV/nucleon}$ . 2. Fusion: $\frac{17.6}{5} \approx 3.52 \text{ MeV/nucleon}$ . 3. Conclusion: Fusion is roughly 4 times more energy-efficient per unit of mass than fission.

Quick Check

What is the primary physical barrier preventing fusion from occurring at room temperature?

Like charges repel.

Answer

The electrostatic (Coulomb) repulsion between the positively charged nuclei.

Fission vs. Fusion: The Global Outlook

While fission is a mature technology providing carbon-free baseload power, it faces challenges regarding radioactive waste with long half-lives and the risk of meltdowns. Fusion is often called the 'holy grail' of energy because its fuel (isotopes of Hydrogen) is abundant in seawater, and its primary byproduct is inert Helium. Fusion reactors cannot melt down because the plasma is so fragile that any disturbance stops the reaction instantly. However, the engineering challenge of maintaining temperatures hotter than the center of the sun ( $>100$ million K) while confining the plasma remains one of the greatest hurdles in modern physics.

In a $D-T$ fusion reaction, the masses are: $m_D = 2.014102 \text{ u}$ , $m_T = 3.016049 \text{ u}$ , $m_{He} = 4.002603 \text{ u}$ , and $m_n = 1.008665 \text{ u}$ . Calculate the energy released in MeV.

1. Calculate initial mass: $M_{in} = 2.014102 + 3.016049 = 5.030151 \text{ u}$ . 2. Calculate final mass: $M_{out} = 4.002603 + 1.008665 = 5.011268 \text{ u}$ . 3. Find mass defect: $\Delta m = 5.030151 - 5.011268 = 0.018883 \text{ u}$ . 4. Convert to energy using $1 \text{ u} = 931.5 \text{ MeV}/c^2$ : $E = 0.018883 \times 931.5 \approx 17.59 \text{ MeV}$ .

Key Takeaways

1Fission involves splitting heavy nuclei (like Uranium) to increase stability, while fusion involves joining light nuclei (like Hydrogen).
2Energy is released in both processes because the products have a higher binding energy per nucleon than the reactants.
3Fusion provides higher energy density and cleaner waste than fission but requires extreme temperatures to overcome Coulomb repulsion.

Quick Check

Multiple Choice

Which component is used in a fission reactor to slow down neutrons so they can be captured by Uranium-235?

Multiple Choice

Why is fusion currently not used for commercial power generation?

True/False

In a nuclear reaction, the total mass of the products is slightly less than the total mass of the reactants.

What's Next?

Review Tomorrow

In 24 hours, try to sketch the Binding Energy per Nucleon curve and identify where Fission and Fusion occur on the graph.

Practice Activity

Research the ITER project—the world's largest experimental fusion reactor—and identify which method of plasma confinement it uses.

Browse

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Nuclear Fission and Fusion

Learning Objectives

Induced Fission and the Binding Energy Curve

Chain Reactions and Criticality

Nuclear Fusion: The Stellar Engine

Fission vs. Fusion: The Global Outlook

Key Takeaways

Quick Check

What's Next?

Nuclear Fission and Fusion

Learning Objectives

Induced Fission and the Binding Energy Curve

Chain Reactions and Criticality

Nuclear Fusion: The Stellar Engine

Fission vs. Fusion: The Global Outlook

Key Takeaways

Quick Check

What's Next?