18 g of silicon-32 will be present in 800 years.
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and it's given by
[tex]N(t) = N_0 (\frac{1}{2}) ^\frac{t}{t_\frac{1}{2} }[/tex]
where,
[tex]N(t) =[/tex] quantity of the substance remaining
[tex]N_0 =[/tex] the initial quantity of the substance
[tex]t =[/tex] time elapsed
[tex]t_1_/_2 =[/tex] the half-life of the substance
From the given information we know:
The initial quantity of silicon-32 is 40 g.
The time elapsed is 800 years.
The half-life of silicone-32 is 710 years.
So, using the calculation above, we can determine how much silicon-32 is left.
[tex]N(t) = 40 (\frac{1}{2}) ^\frac{800}{710} \\N(t) = 40 (\frac{1}{2}) ^\frac{80}{71} \\\\N(t) = 18 g[/tex]
Therefore,18 g of silicon-32 will be present in 800 years.
Learn more about half-life here:
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