Radiactive decay is a reaction of

Options

A. Zero order
B. First order
C. Second order
D. Third order

Answer

To determine the order of radioactive decay, we can follow these steps:

### Step 1: Understand the concept of radioactive decay
Radioactive decay is a process by which unstable atomic nuclei lose energy by emitting radiation. This process results in the transformation of the original nucleus into a different nucleus or a different energy state.

**Hint:** Remember that radioactive decay involves the transformation of nuclei and the emission of radiation.

### Step 2: Analyze the rate of decay
The rate of radioactive decay is defined as the change in the number of radioactive nuclei over time. Mathematically, this can be expressed as:
\[ \frac{dN}{dt} \propto -N \]
where \( N \) is the number of radioactive nuclei present at time \( t \).

**Hint:** Look for how the rate of decay relates to the number of nuclei present.

### Step 3: Introduce the decay constant
To remove the proportionality, we introduce a constant, known as the decay constant (\( \lambda \)):
\[ \frac{dN}{dt} = -\lambda N \]
This equation indicates that the rate of decay is directly proportional to the number of nuclei present.

**Hint:** The decay constant is a key factor in determining the behavior of the decay process.

### Step 4: Identify the order of the reaction
The equation \( \frac{dN}{dt} = -\lambda N \) is characteristic of a first-order reaction. In first-order reactions, the rate of reaction depends linearly on the concentration (or number of nuclei, in this case) of the reactant.

**Hint:** Recall the general form of first-order reactions and how they relate to the concentration of reactants.

### Conclusion
Based on the analysis above, we conclude that radioactive decay is a first-order reaction.

**Final Answer:** Radioactive decay is a first-order reaction.