Question

The half-life of gold-194 is approximately 1.6 days.How much of a 7gram sample of gold-194 would remain after 3days? Round to three decimal places.

Answer 1

Given that the half-life of gold-194 is approximately 1.6 days.

We can find how much of a 7-gram sample of gold-194 would remain after 3days using the formula below;

`\begin{gathered} A=A_0((1)/(2))^{\frac{T}{h_{}}} \\ \text{Where A = final amount}=\text{?} \\ A_0=initial\text{ amout}=7\text{ grams} \\ T\text{ =Time}=3\text{days} \\ h=\text{ half life}=1.6\text{days} \end{gathered}`

We would then substitute the parameters into the formula above.

`\begin{gathered} A=7(0.5)^{(3)/(1.6)} \\ A=7(0.5)^(1.875) \\ A=1.908 \end{gathered}`

Therefore, the amount of a 7gram sample of gold-194 would remain after 3days is;

Answer: 1.908 gram