# Problem: The isotope  208Tl undergoes β decay with a half-life of 3.1 min.(b) How long will it take for 99.0% of a sample of pure 208Tl to decay?

###### FREE Expert Solution

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:

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###### Problem Details

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

(b) How long will it take for 99.0% of a sample of pure 208Tl to decay?