Recall that ** radioactive/nuclear decay of isotopes** follows first-order kinetics, and the integrated rate law for first-order reactions is:

$\overline{){\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{0}}}}$

**Step 1. **Calculate for the decay constant (k):

half-life = **3.1 min**:

The isotope ^{208}Tl undergoes β decay with a half-life of 3.1 min.

(c) What percentage of a sample of pure ^{208}Tl remains un-decayed after 1.0 h?

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