Problem: A certain radioactive nuclide has a half-life of 3.00 hours.b. Calculate the decay rate in decays/s for 1.000 mole of this nuclide.

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FREE Expert Solution

Recall the equation for a first-order half-life:

$\boxed{{\mathbf{t}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}\mathbf{=}\frac{\mathbf{ln}\mathbf{ }\mathbf{2}}{\mathbf{k}}}$

t_1/2 = 3.00 hr

Calculate k:

$$\begin{gathered} \boxed{{\mathbf{t}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}\mathbf{=}\frac{\mathbf{ln}\mathbf{ }\mathbf{2}}{\mathbf{k}}} \\ \mathbf{k}\mathbf{=}\frac{\mathbf{ln}\mathbf{ }\mathbf{2}}{{\mathbf{t}}_{{\displaystyle \raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}}} \\ \mathbf{k}\mathbf{=}\frac{\mathbf{ln}\mathbf{ }\mathbf{2}}{\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{ }\cancel{\mathbf{hr}}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\cancel{\mathbf{hr}}}{\mathbf{60}\mathbf{ }\cancel{\mathbf{min}}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\cancel{\mathbf{min}}}{\mathbf{60}\mathbf{ }\mathbf{s}} \end{gathered}$$

k = 6.418x10^-5 s^-1

Calculate rate: