Problem 117 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statement is/are correct? (a) The decay constant is independent of external factors like temperature and pressure (b) Nuclear isomers have same number of protons and neutrons (c) The decay constant is independent of the amount of the substance used (d) The value of decay constant generally decreases with the rise in temperature

Step-by-Step Solution

Answer

Statements (a), (b), and (c) are correct; statement (d) is incorrect.

Step 1: Understanding Decay Constant

The decay constant (bb) is a factor that represents the probability of a single nucleus decaying per unit time. It is independent of external factors such as temperature and pressure because nuclear decay is a quantum process and doesn't rely on external conditions.

Step 2: Proton and Neutron Count in Isomers

Nuclear isomers are nuclei with the same numbers of protons and neutrons (same mass and atomic numbers) but exist in different energy states due to the arrangement of protons and neutrons within the nucleus.

Step 3: Decay Constant Independency from Amount

The decay constant (bb) is a property of a radioactive substance that remains constant regardless of the amount of the substance. It signifies a constant probability of decay for the nuclei over a given time.

Step 4: Effect of Temperature on Decay Constant

Decay constant is a fundamental property of the nucleus and is generally not affected by changes in temperature. It remains constant because the decay process is not impacted by thermal factors.

Key Concepts

Decay Constant

The decay constant, often symbolized by the Greek letter Lambda (\( \lambda \)), plays a crucial role in understanding nuclear decay. It's a measure of the likelihood that a nucleus will decay per unit time. This probability remains constant over time and does not depend on factors such as temperature or pressure. What this means is that no matter the conditions surrounding a radioactive material, the rate at which it undergoes decay remains the same.

Since nuclear decay is governed by quantum processes, it's insulated from the influences of external variables that might affect chemical reactions. Thus, whether you are deep under the sea or in the heat of a desert, the decay constant for any given substance remains unchanged.

In practical terms:

• A higher decay constant implies a faster decay rate.
• A lower decay constant indicates a slower decay rate.

This consistent behavior of the decay constant is critical for applications like radiometric dating, where precise time measurement is essential.

Nuclear Isomers

Nuclear isomers are fascinating entities in the world of nuclear physics. These are nuclei that share the same numbers of protons and neutrons, yet they exist in different energy states. How is this possible? The secret lies in the arrangement of these particles within the nucleus.

To visualize nuclear isomers, think of them as identical twins with different energy levels. They have:

• The same atomic number, which means the same number of protons.
• The same mass number, indicating an equal total of protons and neutrons.

However, due to different configurations, one might be more energetic than the other. This energy difference can lead to different half-lives and decay paths.

The condition of being in a higher energy state is what makes certain nuclear isomers metastable. Metastable isotopes, such as Technetium-99m, are used in medical imaging owing to their unique decay properties.

Quantum Process

Nuclear decay is fundamentally a quantum process. This means that it operates at the microscopic level of atoms and nuclei, governed by the principles of quantum mechanics. Unlike classical processes, which depend on macroscopic conditions like temperature and pressure, quantum processes are internal to the nucleus.

The unpredictable nature of quantum mechanics implies that, while individual decay events are random, the decay constant provides a reliable statistical measure of decay over a large number of nuclei.

In the realm of quantum mechanics:

• Decisions like whether a nucleus will decay are probabilistic.
• The exact moment of decay for a specific nucleus cannot be predicted.

This inherent unpredictability underlies why nuclear decay is consistent across varying external conditions, as these conditions don't influence the quantum scale processes inside the nucleus.

Quantum processes are central to understanding not just nuclear decay, but the entire behavior of atomic and subatomic particles, highlighting the fascinating intricacies of the microscopic world.