Step 1

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{\mathbf{k}}}\phantom{\rule{0ex}{0ex}}\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{{\mathbf{t}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}}\phantom{\rule{0ex}{0ex}}\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{0}\mathbf{.}\mathbf{693}}{\mathbf{14}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{days}}$

**k = 0.04847 days ^{-1}**

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 Na_{3}^{32}PO_{4} after 35.0 days? Assume the atomic mass of ^{32}P is 32.0 u.