The decay constant related to half`-` life period is `………….`.

Answer

To find the relationship between the decay constant and the half-life period, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Radioactive Decay**:
- Radioactive decay follows first-order kinetics, which means the rate of decay is proportional to the number of radioactive atoms present.

2. **Rate of Disintegration**:
- The rate of disintegration can be expressed mathematically as:
\[ -\frac{dN}{dt} = \lambda N \]
- Here, \( \lambda \) is the decay constant, and \( N \) is the number of radioactive atoms.

3. **Relating Decay Constant to Half-Life**:
- For first-order kinetics, the relationship between the decay constant (\( \lambda \)) and the half-life (\( t_{1/2} \)) can be derived from the formula:
\[ t_{1/2} = \frac{0.693}{\lambda} \]
- This formula shows that the half-life is inversely proportional to the decay constant.

4. **Conclusion**:
- Therefore, the decay constant is related to the half-life period in such a way that:
\[ \text{Decay Constant} \propto \frac{1}{\text{Half-Life Period}} \]
- This means that as the decay constant increases, the half-life decreases, and vice versa.

### Final Answer:
The decay constant related to half-life period is **inversely proportional**.

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