Problem 30 - A Complete Resource Book in Chemistry for JEE Main

Question

\({ }_{1} \mathrm{H}^{1}+{ }_{1} \mathrm{H}^{3} \longrightarrow{ }_{2} \mathrm{He}^{4}\) this represent (a) \(\beta\) decay (b) fusion (c) fission (d) none of these

Step-by-Step Solution

Answer

The reaction represents fusion (b).

Step 1: Understanding the Equation

The equation given is \(_{1} \mathrm{H}^{1}+{ }_{1} \mathrm{H}^{3} \longrightarrow{ }_{2} \mathrm{He}^{4}\). This represents a nuclear reaction where two isotopes of hydrogen, \(^{1}\mathrm{H}\) and \(^{3}\mathrm{H}\), combine to form helium \(^{4}\mathrm{He}\).

Step 2: Identifying the Type of Reaction

In nuclear reactions, fusion occurs when two light atomic nuclei combine to form a heavier nucleus. Here, two hydrogen isotopes are combining to form helium, which is a classic example of nuclear fusion.

Step 3: Reviewing the Options

The options provided are: (a) \(\beta\) decay, (b) fusion, (c) fission, and (d) none of these. \(\beta\) decay involves a neutron changing into a proton (or vice versa) with the emission of an electron (\(\beta^-\)) or a positron (\(\beta^+\)). Fission involves the splitting of a heavy nucleus into lighter nuclei. Fusion involves combining light nuclei to form a heavier nucleus, which matches our reaction.

Key Concepts

Hydrogen Isotopes

Hydrogen isotopes are variants of the hydrogen atom, distinguished by the number of neutrons in their nuclei. Although they have the same number of protons, their differing neutron counts give them unique properties.

• **Protium** - This is the most common hydrogen isotope, denoted by - It has one proton and no neutrons, making it the simplest atom known.
• **Deuterium** - Represented as - It has one proton and one neutron. It is found naturally in water, contributing to what we call "heavy water."
• **Tritium** - Written as - This isotope contains one proton and two neutrons. It is radioactive and is produced in nuclear reactors.

Since protons are positively charged, the difference in the number of neutrons affects the mass and stability of the isotopes. In nuclear fusion reactions, these differences play a critical role in determining how the isotopes combine.

Helium Production

Helium production in stars, such as our Sun, occurs primarily through nuclear fusion. During this process, several smaller nuclei come together to form larger ones. The specific reaction \(_{1} ext{H}^{1} + _{1} ext{H}^{3} ightarrow _{2} ext{He}^{4}\)is an example of such a fusion reaction, where two hydrogen isotopes, protium and tritium, combine to produce helium-4. The process of helium creation through nuclear fusion releases a tremendous amount of energy. This energy is released because the mass of the resulting helium nucleus is slightly less than the sum of the masses of the reacting isotopes. According to Einstein's famous equation \(E=mc^2\), this "missing" mass is converted into energy. This energy is what powers the Sun and other stars, making them shine brightly and emit heat.

Nuclear Reactions

Nuclear reactions involve changes in the atomic nucleus and typically release or absorb large amounts of energy. These reactions can be spontaneous or induced, and they are categorized mainly into fission, fusion, and radioactive decay.

• **Nuclear Fusion** - This is the process where light nuclei combine to form a heavier nucleus. - It requires high temperatures and pressures to overcome electromagnetic repulsion between the positively charged nuclei.
• **Nuclear Fission** - In fission, a heavy nucleus splits into two or more lighter nuclei, along with a few neutrons and a significant amount of energy. This process powers nuclear reactors and atomic bombs.
• **Radioactive Decay** - This is the process by which an unstable atomic nucleus loses energy by emitting radiation. Common types of decay include alpha decay, beta decay, and gamma decay.

Understanding nuclear reactions is key for applications in energy production, medicine, and understanding stellar phenomena. They lie at the core of nuclear physics and help explain how celestial bodies generate immense energy.