The radionuclide ${ }^{\text{56}}\text{Mn}$  is being produced in a cyclotron at a constant rate P by bombarding a manganese target with deuterons (d). ${ }^{\text{56}}\text{Mn}$   has a half-life of 2.5 hours and the target contains large number of only the stable manganese isotope ${ }^{\text{55}}\text{Mn.}$  The reaction that produces  ${ }^{\text{56}}\text{Mn}$  is :
${ }^{\text{55}}\text{Mn+d}{\to }^{56}\text{Mn+p}$
After being bombarded for a long time, the activity of  ${ }^{\text{56}}\text{Mn}$  becomes constant and equal to  $\text{13}.\text{86}\times \text{1}{0}^{\text{1}0} {\text{s}}^{–\text{1}}$.  (Use ln2 = 0.693; Avogadro No $=6\times {10}^{23}$ ; atomic weight ${ }^{56}Mn=56gm/mole$  )