3 Most FAQ’s of Nuclei Chapter in Inter 2nd Year Physics (TS/AP)

8 Marks

LAQ-1 : Explain the principle and working of a nuclear reactor with the help of a labelled diagram.

Introduction

A nuclear reactor is an advanced device designed to produce a significant amount of energy through the process of a controlled chain reaction. Utilizing Uranium, particularly Uranium-238 enriched with Uranium-235, this reaction is carefully managed using specific materials and techniques to ensure safety and efficiency.

Principle of a Nuclear Reactor

The fundamental operation of a nuclear reactor is based on initiating and maintaining a chain reaction within Uranium to release a large quantity of energy. The principle involves:

1. Neutron Moderation: Using a moderator to slow down fast-moving neutrons into thermal neutrons, which then induce the fission of Uranium-235.
2. Reaction Rate Management: Employing control rods made of neutron-absorbing materials to maintain the neutron multiplication factor (K) at 1, ensuring a stable reaction rate.

Working of a Nuclear Reactor

The operation of a nuclear reactor involves several critical steps:

1. Fuel Rods: Containing Uranium are placed within aluminum cylinders.
2. Graphite Moderators: Positioned between fuel cylinders to slow down fast neutrons.
3. Control Rods: Made of Cadmium, Beryllium, or Boron, are inserted into the graphite block to regulate the reaction.
4. Thermal Neutrons Production: Fast neutrons lose energy passing through moderators and become thermal neutrons, which are then absorbed by Uranium-235.
5. Heat Generation: The energy from fission heats coolant (usually water), turning it into steam.
6. Electricity Production: Steam rotates a turbine connected to a generator, producing electricity.

Additional Considerations

1. Cold Water Sink: Essential for maintaining a continuous water flow and absorbing excess heat, which could otherwise impact the surrounding environment.
2. Radiation Containment: Use of materials like lead to absorb radiations emitted during the reaction.
3. Controlled Chain Reaction: Emphasizing the importance of managing the energy produced through precise control mechanisms.

Summary

A nuclear reactor ingeniously utilizes the power of controlled Uranium chain reactions to generate vast amounts of energy. Understanding its principles and operation reveals the complex balance of moderating neutron speeds, controlling reaction rates, and strategically arranging fuel rods, moderators, control rods, and coolants. Safety measures for radiation containment and heat management underline the commitment to safe and efficient nuclear reactor design.

---

LAQ-2 : What is radioactivity ? State the law of radioactive decay. Show that radioactive decay is exponential in nature.

Introduction

Radioactivity is a spontaneous phenomenon where unstable atomic nuclei disintegrate, releasing radiation such as alpha, beta, or gamma rays. This process’s rate is directly proportional to the substance amount present at any given moment, illustrating the core principle of radioactive decay.

The Phenomenon of Radioactivity

1. Radioactivity and the Nucleus: The process is tied to the nucleus’s instability and is unaffected by external conditions like temperature and pressure.
2. Conservation of Charge: The total charge before and after disintegration remains constant, ensuring charge conservation.
3. Emission of Radiation: Disintegration may result in the emission of alpha, beta, and gamma rays, altering the atomic number and weight.
4. Formation of New Elements: The disintegration products are new elements with distinct properties from the parent atom.
5. Statistical Law of Radioactivity: The decay rate is directly proportional to the number of atoms present at a given instant.

Mathematical Explanation of Radioactive Decay

1. Decay Constant: Each substance has a unique decay constant (λ), fundamental to describing its decay rate.
2. Decay Equation: The relationship N = N₀​e^−λt is derived, where N represents the remaining radioactive substances at time t, and N₀​ is the initial amount. This equation showcases an exponential decrease in quantity over time.
3. Half-Life: Defined as the time required for a substance to reduce to half its original value, calculated using $$T_{1/2} = \frac{0.693}{\lambda}$$

Application to a Specific Problem

1. Decay Constant Calculation: Given radium’s half-life of 1600 years, the decay constant λ is determined as $$\lambda = \frac{0.693}{1600}$$
2. Time for Decay: Using the initial amount (1g) and the final amount (0.025g), the time required for decay is calculated to be approximately 3699 years, demonstrating the application of the decay law.

Summary

Radioactivity showcases the disintegration of unstable nuclei, governed by the laws of radioactive decay and characterized by the emission of various types of radiation. By applying principles such as the decay constant and half-life, we can predict and calculate key aspects of radioactive substances’ behavior. Through the example of radium, these concepts provide vital insights into radioactive substances’ nature, emphasizing the importance of understanding exponential decay and the perpetual nature of radioactivity.

---

LAQ-3 : Explain the source of stellar energy. Explain the carbon-nitrogen cycle, proton-proton cycle occurring in stars.

Introduction

Stellar energy is the radiant energy emitted by stars, resulting from nuclear fusion reactions within their cores. These processes involve the fusion of lighter nuclei into heavier nuclei, releasing substantial energy. The Sun is a prime example, utilizing fusion reactions to convert hydrogen into helium, which is the cornerstone of stellar energy production.

Understanding Fusion Reaction

1. Basics of Fusion: Fusion entails the combination of two lighter nuclei to form a heavier, more stable nucleus, which releases energy due to the mass-to-energy conversion principle.
2. Thermonuclear Fusion: This type of fusion, driven by extremely high temperatures, allows lighter nuclei to overcome their mutual repulsion and merge.
3. The Sun’s Fusion Reaction: Predominantly, the Sun achieves hydrogen to helium conversion through the proton-proton cycle, a key fusion process.

Contrast with Other Processes

1. Fission: In contrast to fusion, fission involves the splitting of a heavy nucleus into lighter nuclei, releasing energy.
2. Radioactive Decay: This process involves the spontaneous decay of an unstable nucleus, gradually releasing energy over time.

The Carbon-Nitrogen Cycle and Proton-Proton Cycle

1. Proton-Proton Cycle: This cycle is the primary energy source in stars like the Sun, involving a series of reactions that convert hydrogen into helium.
2. Carbon-Nitrogen Cycle: Also known as the CNO cycle, this process involves carbon acting as a catalyst in the fusion of hydrogen into helium, playing a significant role in more massive stars.

Future of the Sun and Other Stars

1. Sun’s Red Giant Phase: After exhausting its hydrogen fuel, the Sun will expand into a red giant. It has sufficient hydrogen for approximately 5 billion more years of fusion.
2. Formation of Helium and Other Elements: Beyond helium, stars can fuse heavier elements, with processes like the carbon-nitrogen cycle contributing to the synthesis of even more massive elements.

Summary

Stellar energy arises from intricate fusion reactions within stars, transforming hydrogen into helium and other heavier elements. These reactions necessitate extremely high temperatures to overcome nuclear repulsion. As stars evolve, they undergo various phases, with different fusion reactions becoming dominant, leading to the formation of a diverse array of elements. This understanding sheds light on the life cycles of stars and the origin of elements in the universe.