Radioactive decay is a

Options

A. Zero order reaction
B. first order reaction
C. second order reaction
D. Third order reaction

Answer

### Step-by-Step Solution:

1. **Understanding Radioactive Decay**:
Radioactive decay is a process where unstable atomic nuclei lose energy by emitting radiation. This process results in the transformation of the original atom into a different element or a different isotope of the same element.

**Hint**: Remember that radioactive decay involves the transformation of one element into another through the emission of particles or radiation.

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 law. In the case of radioactive decay, we need to determine whether it is a zero-order, first-order, second-order, or third-order reaction.

**Hint**: Consider how the rate of decay depends on the concentration of the radioactive substance.

3. **First-Order Reaction Characteristics**:
Radioactive decay follows first-order kinetics, which means the rate of decay is directly proportional to the number of undecayed nuclei present at any time. The mathematical representation for a first-order reaction is:
\[ N_t = N_0 e^{-\lambda t} \]
where \(N_t\) is the number of undecayed nuclei at time \(t\), \(N_0\) is the initial number of nuclei, and \(\lambda\) is the decay constant.

**Hint**: Recall that in first-order reactions, the rate of reaction decreases as the concentration of the reactant decreases.

4. **Understanding the Decay Constant**:
In radioactive decay, the decay constant (\(\lambda\)) is used instead of the rate constant (\(k\)). The decay constant is unique to each radioactive isotope and indicates the probability of decay per unit time.

**Hint**: Different isotopes have different decay constants, which affect their half-lives.

5. **Half-Life of Radioactive Decay**:
The half-life (\(t_{1/2}\)) of a radioactive substance is the time required for half of the radioactive nuclei in a sample to decay. For first-order reactions, the half-life is given by:
\[ t_{1/2} = \frac{0.693}{\lambda} \]
This formula indicates that the half-life is constant and does not depend on the initial amount of the substance.

**Hint**: The half-life is a crucial concept in understanding the stability and longevity of radioactive materials.

6. **Conclusion**:
Based on the characteristics and equations discussed, we conclude that radioactive decay is a first-order reaction.

**Final Answer**: The correct option is **first-order reaction**.