The decay constant for a radioactive sample containing ¹²⁸ I is found to be approximately 0.028 min ⁻¹ . Calculate the half-life t_ 1/2 . Time t (minute) 0 25 50 75 100 Count rate R ( 10⁹ s ⁻¹ ) 30 16 8.0 3.8 2.0

Step-by-step solution

The relation between half-life t_ 1/2 and decay constant is given by: t_ 1/2 = 2 Substituting = 0.028 min ⁻¹ : t_ 1/2 = 0.693 0.028 = 24.75 min 25 min Alternatively, observing the given table, the count rate R becomes approximately half of its value after every 25 min . For instance, at t = 25 min , R = 16 10⁹ s ⁻¹ which is roughly half of the initial value 30 10⁹ s ⁻¹ . At t = 50 min , R = 8.0 10⁹ s ⁻¹ which is exactly half of 16 10⁹ s ⁻¹ . Thus, the half-life is 25 min .