Obtain the relation `N=N_(0)e^(-lamdat)` for a sample of radio active material having decay constant `lamda` where N is the number of nuclei present at instant t. Hence, obtain the relation between decay constant `lamda` and half life `T_(1//2)` of the sample.

Explanation

To derive the relation \( N = N_0 e^{-\lambda t} \) for a sample of radioactive material with decay constant \( \lambda \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Decay Process**:
- Let \( N_0 \) be the initial number of radioactive nuclei at time \( t = 0 \).
- Let \( N(t) \) be the number of radioactive nuclei remaining at time \( t \).

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