Radioactive material undergoes first order dissociation kinetics.
For 1st order system,
k = 0.693 / t1/2
where, t 1/2 = half-life of the radioactive disintegration process.
Given that, t 1/2 = 73.83 days
Therefore, k = 0.009386 day-1
Also, for 1st order reaction,
k = [tex] \frac{2.303}{t} log \frac{Co}{Ct} [/tex]
Given that, Co = initial concentration of Iridium-192 = 100 g
Therefore, 0.009386 = [tex] \frac{2.303}{t} log \frac{100}{Ct} [/tex]
On rearranging we get, Ct = 100 [tex] (0.990656)^{t} [/tex]
Answer: Ct = 100 [tex] (0.990656)^{t} [/tex] equation approximates the amount of Iridium-192 present after t days
