# How long must a sample be irradiated before all 59-Co atoms are converted to 60-Co? [closed]

For the interaction, n$^0$ + $^{59}$Co $\to$ $^{60}$Co

## closed as off-topic by Michael DM Dryden, Jannis Andreska, Jason Patterson, Freddy, user7232 Oct 7 '14 at 18:14

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$- \frac{{{\text{d}}\left[ {{}^{59}{\text{Co}}} \right]}}{{{\text{d}}t}} = k \cdot \left[ {{}^{59}{\text{Co}}} \right]$
$\left[ {{}^{59}{\text{Co}}} \right] = {\left[ {{}^{59}{\text{Co}}} \right]_0} \cdot {\operatorname{e} ^{ - k \cdot t}}$
Theoretically, $\left[ {{}^{59}{\text{Co}}} \right]$ will never become zero.