Answer
14.3 days.
Work Step by Step
Amount of radionuclide at the beginning $A_{0}=1.2\,mg$
Amount of radionuclide remaining
$A=0.30\,mg$
Time $t=28.6\,d$
$\ln(\frac{A_{0}}{A})=kt=\frac{0.693}{t_{1/2}}\times t$
$\implies \ln(\frac{1.2}{0.30})=1.386=\frac{0.693}{t_{1/2}}\times28.6\,d$
Then, $t_{1/2}=\frac{0.693\times28.6\,d}{1.386}=14.3\,d$
