Answer:
[tex]57.7[/tex] grams
Explanation:
Given -
Half life of the silicon-32 [tex]= 710[/tex] years
Half life means the time period required by a radioactive element to reduce its mass by half.
Radioactive decay formula is
[tex]A = A_o*2^{\frac{-t}{h} }[/tex]
Where
A represents the amount of radioactive element after time t years
[tex]A_0[/tex] represents the initial amount of radioactive element
[tex]t =[/tex] time of decay
[tex]h =[/tex] half-life of the substance
Substituting the given values in above equation, we get -
[tex]A = 70 * 2^{\frac{200}{710} \\[/tex]
[tex]A = 57.7[/tex] grams
The amount that will be present in 200 years is 57.584 g
We'll begin by calculating the number of half-lives that has elapsed.
Half-life (t½) = 710 years
Time (t) = 200 years
n = t / t½
n = 200 / 710
Number of half-lives (n) = 20/71
Initial amount (N₀) = 70 g
[tex]N = \frac{N_0}{ {2}^{n} }\\ \\ N = \frac{70}{ {2}^{20 \div 71} } \\ \\ N = 57.584 \: g[/tex]
Thus, the amount remaining after 200 years is 57.584 g
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