Question

Explain how it is possible that fission, the splitting of nuclei, and fusion, the combining of nuclei, both release tremendous amounts of energy.

Short answer

In both nuclear fission and fusion, tremendous amounts of energy are released due to the change in binding energy per nucleon which makes the resulting nuclei more stable. In fission, a heavy nucleus splits into smaller nuclei, while in fusion, lighter nuclei combine to form a heavier nucleus. The mass defect associated with these reactions, due to the small decrease in total mass, is converted into energy according to Einstein's mass-energy equivalence principle (\(E=mc^2\)), leading to the significant energy output in both processes.

Step-by-step solution

Nuclear Fission

Nuclear fission occurs when the nucleus of an atom splits into smaller parts. This usually happens due to the absorption of a low-energy neutron by a heavy atomic nucleus, which becomes unstable and splits into two or more smaller nuclei along with the release of a large amount of energy and more neutrons. These new neutrons can then initiate the fission of other heavy nuclei, leading to a chain reaction.

Energy Release in Fission

The energy released in nuclear fission is due to the difference in binding energy between the heavier nucleus and the smaller nuclei formed. Binding energy is the energy required to keep protons and neutrons together within a nucleus. The binding energy per nucleon increases initially with increasing atomic mass and reaches a maximum at the nuclei with around atomic mass A≈60 and then decreases for heavier nuclei. In a fission reaction, the binding energy per nucleon of the resulting smaller nuclei is higher than the initial heavy nucleus, which means they are more stable. The difference in binding energy is released as the energy in the form of kinetic energy, gamma rays, and the emission of neutrons.

Nuclear Fusion

Nuclear fusion is the process where two or more smaller atomic nuclei come together to form a larger nucleus. This process generally occurs at very high temperatures and pressures. In stars, hydrogen nuclei (protons) fuse together to form helium nuclei, releasing a tremendous amount of energy in the form of light and heat.

Energy Release in Fusion

Similar to fission, the energy released in nuclear fusion comes from the difference in binding energy between the initial lighter nuclei and the resulting heavier nucleus. In the case of fusion, the binding energy per nucleon increases with mass for light elements, reaching a maximum at around A≈60. So when light nuclei combine to form heavier nuclei, the binding energy per nucleon increases, leading to a release of energy in the form of kinetic energy and electromagnetic radiation.

Mass-Energy Equivalence

According to Einstein's famous equation \(E=mc^2\), energy and mass are directly related. In both fission and fusion reactions, there is a small decrease in the total mass of the reacting nuclei and particles, which is known as the mass defect. This mass is converted into energy and released during the reaction. As the speed of light (c) is a very large number, even a small mass defect results in a significant amount of energy being released. In conclusion, both nuclear fission and fusion reactions involve the release of tremendous amounts of energy due to changes in binding energy per nucleon, making the resulting nuclei more stable. The mass defect associated with these reactions is converted into energy according to Einstein's mass-energy equivalence principle, leading to the vast energy output observed in both processes.

Key concepts

Nuclear Fission

Nuclear fission is the process where the nucleus of a heavy atom, like uranium or plutonium, splits into smaller parts. This usually happens when the nucleus absorbs a slow-moving neutron. When the nucleus splits, it releases not only energy but also more neutrons. These new neutrons can then cause additional fission in nearby nuclei, potentially leading to a chain reaction.
This chain reaction is what powers nuclear reactors and atomic bombs. The key to fission is the balance of protons and neutrons in the nucleus, which can become unstable when disrupted.

• The starting nucleus is large and heavy.
• Neutrons released can initiate further fission.
• Leads to a controlled or uncontrolled chain reaction.

Nuclear Fusion

Nuclear fusion occurs when two or more light atomic nuclei combine to form a heavier nucleus. This process occurs naturally in stars, where hydrogen atoms fuse to form helium, releasing a vast amount of energy. Fusion requires extremely high temperatures and pressures to overcome the repulsive forces between the positively charged nuclei.
The Sun, our closest star, is a perfect example of nuclear fusion at work. Here, the energy produced keeps the star shining and providing warmth to our solar system.

• Involves light nuclei like hydrogen or helium.
• Requires high temperature and pressure.
• Powers stars and has potential for sustainable energy on Earth.

Binding Energy

Binding energy is the energy needed to hold a nucleus together, keeping its protons and neutrons in place. It is a measure of stability for a nucleus, with higher binding energy indicating greater stability. In nuclear reactions, energy changes occur due to differences in binding energy.
When a nucleus undergoes fission or fusion, the binding energy differences between the reactants and products result in energy release.

• Higher binding energy means more stability.
• Key factor in energy change during nuclear reactions.
• Understanding binding energy helps explain why fission and fusion release energy.

Mass-Energy Equivalence

Einstein's equation, \(E=mc^2\), is central to nuclear reactions. It tells us that mass and energy are interchangeable. In both nuclear fission and fusion, a small amount of mass is converted into a large amount of energy. This is called the "mass defect."
Due to the enormous value of the speed of light squared, even tiny mass changes result in significant energy releases.

• Small mass changes result in large energy output.
• Explains the high energy release in nuclear reactions.
• Part of the reason why stars shine and nuclear power works.

Chain Reaction

A chain reaction occurs when a single nuclear reaction causes additional reactions to occur, leading to a self-sustaining process. In fission reactions, the neutrons released can initiate other fissions, creating a series of reactions.
This concept is crucial in nuclear reactors where the reaction must be controlled, and in nuclear weapons where it occurs rapidly and uncontrollably.

• Essential for sustained energy production in nuclear reactors.
• Requires careful control to avoid explosions in nuclear plants.
• Example: The splitting of uranium in reactors or bombs.