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]

Determine the concentrations of I135 and Xe135 as functions of time following shutdown by determining
(a) The transition matrix and the system response.
(b) Verify that the response of the system is that shown in Figure P3.20.
Figure P3.20
Nuclear reactor response.

0.693 6.7 x 0.693 9.2 X.I 7 x Xenon 135 rodine 135 10I5 C0 0 5 250 40 2 Time (t in hours