Given data
*The half-life time of polonium-239 is T = 24,300 years
*The nuclear bomb released the isotope is N = 8 kg
*The reduced amount is N(t) = 4.00 kg
From the radioactive decay equation, it is given as
[tex]N(t)=N(\frac{1}{2})^{\frac{t}{T}}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} 4.0=8(\frac{1}{2})^{\frac{t}{24300}} \\ t=24300 \end{gathered}[/tex]