How long must a sample be irradiated before all 59-Co atoms are converted to 60-Co?
At a constant neutron flux, this is a first-order reaction:

$ - \frac{{{\text{d}}\left[ {{}^{59}{\text{Co}}} \right]}}{{{\text{d}}t}} = k \cdot \left[ {{}^{59}{\text{Co}}} \right]$

$\left[ {{}^{59}{\text{Co}}} \right] = {\left[ {{}^{59}{\text{Co}}} \right]_0} \cdot {\operatorname{e} ^{ - k \cdot t}}$

Theoretically, $\left[ {{}^{59}{\text{Co}}} \right]$ will never become zero.