The decay constant λ for a radioactive sample containing ^ 128 I is...

The relation between half-life $t_{1/2}$ and decay constant $\lambda$ is given by:

$t_{1/2} = \dfrac{\ln 2}{\lambda}$

Substituting $\lambda = 0.028 \text{ min}^{-1}$:

$t_{1/2} = \dfrac{0.693}{0.028} = 24.75 \text{ min} \approx 25 \text{ min}$

Alternatively, observing the given table, the count rate $R$ becomes approximately half of its value after every $25 \text{ min}$. For instance, at $t = 25 \text{ min}$, $R = 16 \times 10^{9} \text{ s}^{-1}$ which is roughly half of the initial value $30 \times 10^{9} \text{ s}^{-1}$. At $t = 50 \text{ min}$, $R = 8.0 \times 10^{9} \text{ s}^{-1}$ which is exactly half of $16 \times 10^{9} \text{ s}^{-1}$.

Thus, the half-life is $25 \text{ min}$.