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The half-life of polonium-239 is 24,300 years. If a nuclear bomb released 8.00 kg of this isotope, how many years would pass before the amount is reduced to 4.00 kg?

Answer :

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]

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