Question

Which of the following is a fusion reaction? (a) \({ }_{98} \mathrm{U}^{255}+{ }_{0} \mathrm{n}^{1} \longrightarrow{ }_{36} \mathrm{Ba}^{141}+{ }_{36} \mathrm{Kr}^{92}+3_{0} \mathrm{n}^{1}\) (b) \({ }_{92} \mathrm{Fe}^{259}+{ }_{0} \mathrm{n}^{1} \longrightarrow{ }_{92} \mathrm{U}^{239}+\mathrm{Y}\) (c) \({ }_{26} \mathrm{Fe}^{55}+{ }_{-1} \mathrm{e}^{0} \longrightarrow{ }_{25} \mathrm{Mn}^{55}\) (d) \({ }_{1} \mathrm{H}^{1}+{ }_{1} \mathrm{H}^{1}+2 \underset{0}{\mathrm{n}}^{1} \longrightarrow \mathrm{He}^{4}+\) energy

Short answer

Option (d) is a fusion reaction.

Step-by-step solution

Understanding Fusion Reactions

Fusion reactions involve the combining of two light atomic nuclei to form a heavier nucleus. Fusion is characterized by the release of a significant amount of energy due to the binding energy of the new nucleus formed.

Analyze Each Option

We need to identify which given nuclear reaction involves the fusion of light nuclei. - (a) is a fission reaction as it involves the splitting of a heavy nucleus. - (b) is a neutron capture reaction with no fusion. - (c) is a beta decay reaction. - (d) involves two hydrogen nuclei combining to form helium, characteristic of fusion.

Identify Characteristics of Option (d)

In reaction (d), two hydrogen nuclei, \(_{1} \mathrm{H}^{1}\), combine. This is a hallmark of fusion as they form helium \( \mathrm{He}^{4}\) and release energy due to the high binding energy of the helium nucleus, which confirms it as a fusion reaction.

Key concepts

Nuclear Reactions

Nuclear reactions involve changes in an atom's nucleus and can lead to the release or absorption of energy. They are distinct from chemical reactions, which involve the rearrangement of electrons. In nuclear reactions, such as fusion and fission, atomic nuclei either combine or break apart to form new nuclei.

• Fusion: This is the process where two lighter atomic nuclei come together to form a heavier nucleus. It usually occurs at extremely high temperatures and pressures, like in stars.
• Fission: In contrast, fission involves a heavy nucleus splitting into two or more lighter nuclei.
  The type of nuclear reaction is determined by whether the process involves the merging or splitting of nuclei, as well as the types and amounts of energy produced or consumed.

Binding Energy

Binding energy is the energy required to either separate a nucleus into its individual protons and neutrons or, conversely, the energy released when a nucleus forms from these components. When a nuclear reaction such as fusion occurs, a new heavier nucleus is formed which is incredibly stable due to its high binding energy.
The importance of binding energy in fusion reactions lies in the fact that when small nuclei combine, the resulting nucleus has a higher binding energy than the original nuclei. This results in a release of energy, which is why fusion is considered a powerful energy source.
In

• Fusion reactions: The binding energy of the formed nuclei is greater than the sum of the binding energies of the original nuclei, thus releasing energy.
• Fission reactions: The reverse is often true; breaking apart heavy nuclei can release significant amounts of energy due to changes in binding energy.

Hydrogen Nuclei

At the heart of fusion reactions is the hydrogen nucleus, which is the simplest and lightest element. A hydrogen nucleus, also known as a proton, is central in forming heavier elements through nuclear fusion. This is because of its ability to combine with another hydrogen nucleus to form helium.
Protons within hydrogen nuclei possess a positive charge and repel each other due to electromagnetic forces. However, under the extreme conditions of high temperature and pressure, like those found in the sun, protons can overcome their repulsion and get close enough for the strong nuclear force to bind them together.

• This process is responsible for energy generation not only in the sun but also in hydrogen bombs and potential future fusion reactors.
• The fusion of hydrogen nuclei is sustainable because it uses water isotopes, deuterium, and tritium, making the process have minimal long-term radioactive waste when compared to traditional fission reactions.

Helium Formation

Helium formation occurs when hydrogen nuclei, or protons, fuse under extreme conditions. This process is the core reaction in stars, including our sun, to produce energy. During this fusion process, several crucial transformations occur.
In a typical fusion reaction like the one given in the exercise, two hydrogen nuclei combine to form a helium nucleus. This is represented in nuclear notation as i.e., i.e., \(\_{1} \mathrm{H}^{1} + \_{1} \mathrm{H}^{1} \rightarrow \mathrm{He}^{4}\). Here, the subscript denotes the atomic number (number of protons), and the superscript indicates the mass number (total number of protons and neutrons). The resulting helium nucleus has a higher binding energy and the reaction releases a substantial amount of energy.

• This process converts a small amount of mass into energy according to Einstein’s mass-energy equivalence principle \( E = mc^2 \).
• Helium formation through fusion is efficient and results in a loss of mass, which is converted into energy observed as light and heat from stars.