Problem 20 - A Complete Resource Book in Chemistry for JEE Main

Question

Decay of \(_{92} \mathrm{U}^{235}\) is \(\ldots \ldots\) order reaction (a) first (b) second (c) third (d) zero

Step-by-Step Solution

Answer

The decay of (_{92}U^{235}) is a first-order reaction.

Step 1: Understanding the Concept of Nuclear Decay

The decay of a radioactive isotope like (_{92}U^{235}) involves the transformation of an unstable nucleus into a more stable nucleus through emitting particles, often alpha or beta particles. Radioactive decay is a spontaneous process that can be represented by a specific order of reaction based on the half-life dependence on the concentration of the remaining isotope.

Step 2: Identifying the Order of Reaction for Radioactive Decay

Radioactive decay is commonly a first-order process. This means the rate of decay is directly proportional to the number of undecayed nuclei present. The general feature of first-order reactions is that the half-life does not depend on the initial concentration, which fits the nature of nuclear decay well.

Step 3: Applying the First-Order Reaction Knowledge

For any first-order reaction, the rate (R) can be expressed as (R = k [N]), where (k) is the decay constant and ([N]) is the concentration of the reacting nucleus. In radioactive decay, the rate at which (_{92}U^{235}) decays is proportional to the remaining amount of (_{92}U^{235}) atom.

Step 4: Final Conclusion on the Order of Reaction

Since the rate of decay follows first-order kinetics, the decay of (_{92}U^{235}) must be a first-order reaction. This confirms that the decay process does not depend on the concentration of the remaining substance involved in the reaction in terms of its half-life pattern.

Key Concepts

First-Order Reaction

In chemistry, many reactions are classified by their order, which describes how the rate of the reaction depends on the concentration of the reactants. In first-order reactions, the rate is directly proportional to the concentration of one reactant. The decay of radioactive substances, like uranium-235, is frequently a first-order process. This is due to how the reaction progresses over time. The rate equation for a first-order reaction is given by \( R = k [A] \), where \( R \) is the rate of the reaction, \( k \) is the decay constant, and \( [A] \) is the concentration of the substance undergoing reaction.

Due to this dependency, even if the concentration of the substance decreases, the rate of reaction adjusts proportionally, sticking to its first-order behavior. An essential feature of first-order reactions is that their half-life, the time it takes for half of the radioactive atoms to decay, remains constant regardless of the initial concentration of the reactant.

This characteristic fits radioactive decay perfectly, allowing predictability in processes ranging from dating ancient artifacts to understanding nuclear power dynamics.

Nuclear Chemistry

Nuclear chemistry is a field that investigates the changes and reactions involving atomic nuclei. It plays an intriguing role in understanding the nature of radioactive decay. When we study nuclear chemistry, we explore how unstable nuclei transform by emitting energy in the form of radiation to achieve greater stability. This is the core principle behind radioactive decay.

Radioactive isotopes, such as \( _{92}\mathrm{U}^{235} \), undergo nuclear reactions to accomplish a more stable state. During these decay processes, particles like alpha and beta particles, or even gamma rays, are emitted. This emission leads to a transformation in the composition of the nuclide. It's fascinating because this transformation is not about chemical bonds but changes within the atom's core nucleus.

Nuclear chemistry helps us understand tremendous energy releases, seen in nuclear power plants, medical imaging, and even treatments for cancer.

• It provides insights into nuclear stability.
• Explains transmutation reactions where one element becomes another.
• Clarifies how and why certain isotopes are radioactive.

With this field's knowledge, we can harness nuclear reactions safely and effectively.

Decay Constant

The decay constant is a crucial parameter in understanding radioactive decay, representing the probability of a particular nucleus decaying per unit time. In the equation \( R = k [N] \), \( k \) symbolizes the decay constant, correlating directly to the half-life of the isotope in question.

For first-order reactions, including nuclear decay, the half-life is inversely related to the decay constant: \( t_{1/2} = \frac{0.693}{k} \). This means that a higher decay constant implies a shorter half-life, as the substance decays more rapidly.

The decay constant is significant because it allows scientists to predict how long a sample of a radioactive isotope will remain active. It is foundational in fields such as:

• Radiometric dating, allowing us to determine the age of archaeological finds.
• Nuclear medicine, optimizing the timing and dosage of radioisotopes for diagnostics and treatment.
• Environmental science, studying the longevity of nuclear waste products.

Understanding the decay constant not only enables precise calculations related to the lifespan and behavior of isotopes but also assists in evaluating risks and planning uses for radioactive materials.