State the law of radioactive decay. Plot a graph showing the number (N) of undecayed nuclei as a function of time (t) for a given radioactive sample having half life `T_(1//2)`
Depict in the plot the number of undecayed nuclei at
(i) `t=3T_(1//2)` and (ii) `t=5T_(1//2)`.

Explanation

### Step-by-Step Solution

**Step 1: State the Law of Radioactive Decay**

The law of radioactive decay states that the rate of decay of a radioactive substance is directly proportional to the number of undecayed nuclei present at any given time. Mathematically, this can be expressed as:

\[
\frac{dN}{dt} = -\lambda N
...