Problem: Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus-32 is left from an original sample of 175 mg Na332PO4 after 35.0 days? Assume the atomic mass of 32P is 32.0 u.

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Step 1

$$\begin{gathered} \boxed{{\mathbf{t}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{ln}\mathbf{ }\mathbf{2}}{\mathbf{k}}} \\ \mathbf{k}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{ln}\mathbf{ }\mathbf{2}}{{\mathbf{t}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}} \\ \mathbf{k}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{0}\mathbf{.}\mathbf{693}}{\mathbf{14}\mathbf{.}\mathbf{3}\mathbf{ }\mathbf{days}} \end{gathered}$$

k = 0.04847 days^-1