Problem 21 - A Complete Resource Book in Chemistry for JEE Main

Question

Order of radioactive disintegration reaction is (a) third (b) second (c) first (d) zero

Step-by-Step Solution

Answer

The order of radioactive disintegration reaction is first (c).

Step 1: Understanding Radioactive Disintegration

Radioactive disintegration, or decay, is a process by which an unstable atomic nucleus loses energy by radiation. This process can be described mathematically by its rate equation, which is characteristic of its order.

Step 2: Identifying the Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate equation. Radioactive disintegration follows a unique first-order kinetics, meaning the rate of reaction is proportional to the concentration of a single reactant.

Step 3: First-Order Kinetics Explanation

In first-order kinetics, the rate of decay is directly proportional to the number of undecayed nuclei present. The mathematical expression is: \[ Rate = k [N] \] where \( k \) is the decay constant and \( [N]\) is the concentration of the nuclei.

Key Concepts

First-Order Kinetics

Imagine a process where the amount of a substance diminishes over time. This is what happens in first-order kinetics. Specifically, in the context of radioactive disintegration, it means that the rate at which the nucleus decays is directly tied to the number of radioactive atoms still present. This is quite definitive because first-order kinetics help predict how quickly a substance will decay.

The defining mathematical expression for first-order kinetics is:

• Rate = k [N]

Here, the rate is how fast the disintegration happens, which is proportional to the concentration of the undecayed radioactive material. This linear relationship simplifies calculations and predictions about the nuclear decay process.

Rate Equation

The rate equation in radioactive decay is a fundamental tool in understanding how nuclear reactions unfold over time. It relates the rate of a radioactive process to the concentration of the reactant.

For a first-order reaction, the rate equation can be represented as:

• \[ Rate = k [N] \]

In this formula:

• Rate is how quickly the substance is converting.
• k is the decay constant, which is specific to each radioactive substance.
• [N] stands for the concentration of nuclear species that hasn't decayed yet.

This equation captures the essence of radioactive decay by demonstrating that the speed of the reaction is directly proportional to the amount of substance present at any time.

Reaction Order

Reaction order is a critical concept in chemistry, indicating the power to which the concentration of a reactant is raised in the rate law. For radioactive disintegration, the reaction order is one, meaning it is a first-order reaction. This implies that the concentration's direct relationship to the rate is linear.

Understanding reaction order allows us to predict how changing concentrations affect reaction rates. In the context of radioactive materials, knowing the process follows first-order kinetics allows us to utilize simple and straightforward calculations to determine decay over time.

Decay Constant

The decay constant, denoted as \( k \), is an essential factor in the calculation of how quickly radioactive substances change. It represents the probability per unit time that a given nucleus will decay. Each radioactive element has its unique decay constant, which reflects different rates of nuclear disintegration.

Mathematically:

• The larger the value of \( k \), the quicker the decay occurs.
• This constant directly affects how we calculate the remaining concentration of radioactive material over time, giving insights into the half-life of a substance.

Overall, the decay constant provides critical information needed to quantify and predict the behavior of radioactive substances under first-order kinetics.