Define the term 'decay constant' of a radioactive sample. The disintegration of a given radioactive nucleus is `10000` disintegrations/s and `5,000` disintegration/s after `20 hr` and `30 hr` respectively from start. Calculate the half life and initial number of nuclei at `t = 0`.

Explanation

### Step-by-Step Solution

1. **Define Decay Constant**:
The decay constant (λ) of a radioactive sample is defined as the ratio of the rate of change of the number of radioactive nuclei at any given time to the number of nuclei present at that time. Mathematically, it is expressed as:
\[ \lambda = -\frac{dN}{dt} \cdot \frac{1}{N} \]
where \(N\) is the number of radioactive nuclei.
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