Answer:
22.38 g of silicone-32 will be present in 300 years.
Step-by-step explanation:
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by
[tex]N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{1/2}}[/tex]
where,
[tex]N(t)[/tex] = quantity of the substance remaining
[tex]N_0[/tex] = initial quantity of the substance
[tex]t[/tex] = time elapsed
[tex]t_{1/2}[/tex] = half life of the substance
From the information given we know:
So, to find the quantity of silicone-32 remaining we apply the above equation
[tex]N(t)=30\left(\frac{1}{2}\right)^{\frac{300}{710}}=30\left(\frac{1}{2}\right)^{\frac{30}{71}}\approx22.38 \:g[/tex]
22.38 g of silicone-32 will be present in 300 years.
silicone commonly referred to as siloxane is any of a diverse variety of fluid, resins, or elastomers based on polymerized siloxanes, compounds whose molecules are made up of consecutive silicon and oxygen atoms.
Following are the calculation to the silicone life:
[tex]A(t) = A_0\times (\frac{1}{2})^{\frac{t}{710} \ \ \ \ \ \ \ where: \\[/tex]
[tex]A(t) = \text{the amount left in t years}\\\\A0 = \text{the initial amount} = 30 g\\\\t = years = 300\\\\[/tex]
Solution:
[tex]\to A(300) = (30 \ g) \times (\frac{1}{2})^{\frac{300}{710}}\\\\[/tex]
[tex]= (30 \ g) \times (\frac{1}{2})^{\frac{30}{71}}\\\\ = (30 \ g) \times (0.5)^{0.422}\\\\ = 30 \ g \times 0.746\\\\=22.38 \ g[/tex]
Therefore, the final answer is "22.38 g".
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