A nuclear reactor that has been operating in equilibrium at a high thermal-neutron flux level is suddenly shut down. At shutdown, the density X of xenon 135 and the density I of iodine 135 are 7×1016 and 3×1015 atoms per unit volume, respectively. The half-lives of I135 and Xe135 nucleides are 6.7 and 9.2 hours, respectively.

The decay equations are [15, 19]

1(t)= 0.693 6.7 I(t), X(t)=- 0.693 9.2 X(t)- I(t). Determine the concentrations of I135 and Xe135 as functions of time following shutdown by determin- ing (a) the transition matrix and the system response. (b) Verify that the response of the system is that shown in Figure P3.20.