Problem 67 - Master Resource Book in JEE Main Physics

Question

Match the following Column I with Column II Column I \(\quad\) Column II Column 1. I. Nuclear fusion II. Mass defect III. Nuclear reaction IV. Nuclear reactor Column II A. \(E=m c^{2}\) B. Moderator C. Stellar energy D. Binding energy Codes (a) I-C, II-D, III-A, IV-B (b) I-A, II-B, III-C, IV-D (c) II-D, I-A, III-C, IV-A (d) I-C, II-B, III-A, IV-D

Step-by-Step Solution

Answer

The correct matching is option (a): I-C, II-D, III-A, IV-B.

Step 1: Understand the Concept of Nuclear Fusion

Nuclear fusion is a reaction where two light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. This process primarily occurs in stars and accounts for their energy generation. Therefore, nuclear fusion matches with "C. Stellar energy."

Step 2: Understand the concept of Mass Defect

Mass defect refers to the discrepancy between the mass of a nucleus and the sum of the masses of its constituent nucleons. This is related to the energy released during nuclear reactions, described by "D. Binding energy." Hence, mass defect matches with "II-D".

Step 3: Comprehend Nuclear Reaction

A nuclear reaction involves changes in an atom's nucleus. According to Einstein's equation, the energy produced during this change can be calculated using the famous equation "E=mc^2." Therefore, nuclear reaction corresponds with "A. E=mc^2."

Step 4: Identify Components of a Nuclear Reactor

A nuclear reactor is a system that contains and controls nuclear reactions. A moderator is a substance used to slow down neutrons in a reactor to sustain the reaction chain. Thus, nuclear reactor aligns with "B. Moderator."

Step 5: Match Each Item with Correct Code

From the analysis, we have: I-C (Nuclear fusion - Stellar energy), II-D (Mass defect - Binding energy), III-A (Nuclear reaction - E=mc^2), IV-B (Nuclear reactor - Moderator). Therefore, the correct code matches choice (a).

Key Concepts

Nuclear Fusion

Nuclear fusion is a process where two light atomic nuclei join to form a single heavier nucleus. This reaction releases a significant amount of energy. It is the same process that powers the stars, including our Sun.
In a nuclear fusion reaction, hydrogen isotopes combine to form helium, a heavier element, along with a burst of energy. This energy is due to the loss of mass during the fusion, as described by Einstein's famous equation:

• Fusion occurs naturally in stars.
• It is a potential source of almost limitless energy.
• The process requires extremely high temperatures and pressures.

The energy generated by nuclear fusion is what keeps stars shining for billions of years.

Mass Defect

Mass defect is an interesting concept in nuclear physics. It refers to the difference between the total mass of an atomic nucleus and the sum of the individual masses of its protons and neutrons. This difference is important because it represents the energy released when the nucleus is formed. In simpler terms, the missing mass has been converted to energy, which is released as binding energy. Binding energy is crucial as it holds the nucleus together and is calculated using the formula:\[E=mc^2\]Here, \(m\) is the mass defect, and \(c\) is the speed of light. The equation shows the equivalence between mass and energy.

Nuclear Reaction

A nuclear reaction involves changes within an atom's nucleus. This can include processes like nuclear decay, fission, or fusion. Nuclear reactions are powerful because they can release immense amounts of energy. Einstein’s equation, \(E=mc^2\), is fundamental to understanding these reactions. It explains how a small amount of mass can be converted into a large amount of energy during such changes. There are different types of nuclear reactions, such as:

• Nuclear Fission: the splitting of a large nucleus into smaller ones.
• Nuclear Fusion: combining small nuclei to form larger ones.
• Radioactive Decay: the process where unstable nuclei lose energy.

Each type of reaction has different applications, from nuclear power plants to medical treatments.

Nuclear Reactor

A nuclear reactor is an engineered system designed to initiate and control nuclear reactions, primarily for energy generation. It harnesses the energy from nuclear reactions to produce electricity. Within a nuclear reactor, components like the moderator play a crucial role. They slow down fast neutrons, making them more effective in sustaining the ongoing nuclear chain reactions. Nuclear reactors have several key components:

• Fuel: typically consists of uranium or plutonium isotopes.
• Moderator: slows down neutrons to sustain the chain reaction.
• Control Rods: absorb neutrons to regulate the reaction rate.
• Coolant: removes heat from the reactor core.

Nuclear reactors must be carefully managed to maintain safety and efficiency.