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Answer :
[tex]N(t)=N_{\circ}(\frac{1}{2})^{\frac{t}{t_{\circ}}}[/tex][tex]\begin{gathered} \text{where} \\ N(t)=quantity\text{ remaining} \\ N_{\circ}=Initial\text{ substance} \\ t=time\text{ elapsed} \\ t_{\circ}=half\text{ life} \end{gathered}[/tex][tex]\begin{gathered} N(t)=12.5g \\ N_{\circ}=100g \\ t=25.3\text{ days} \\ t_{\circ}=? \end{gathered}[/tex][tex]undefined[/tex]
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Final answer:
The half-life of gold-198 is approximately 8.43 days.
Explanation:
The half-life of a radioactive isotope is the time it takes for half of the sample to decay. In this case, the initial amount of gold-198 is 100 g and it decays to 12.5 g in 25.3 days. To find the half-life, we can use the formula:
Half-life = (time elapsed − time remaining) / log2 (initial amount / remaining amount)
Plugging in the values: Half-life = (25.3 days − 0 days) / log2 (100 g / 12.5 g) = 25.3 days / log2 (8) = 25.3 days / 3
So, the half-life of gold-198 is approximately 8.43 days.
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