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Sagot :
Given :
The half-life of carbon 14 is 5,730 years.
To Find :
How much would be left of an original 50- gram sample after 2, 292 years.
Solution :
We know, rate law for first order reaction is given by :
[tex][A] = [A_o]e^{-kt}[/tex] ...1)
Here, [tex]A_o[/tex] is initial amount and [tex]A[/tex] is final amount.
And [tex]k = \dfrac{ln\ 2}{t_{0.5}}[/tex]
Putting value of half time in above equation, we get :
[tex]k = \dfrac{ln\ 2}{5730}\\\\k = 1.21\times10^{-4} \ /s[/tex]
Putting value of k in equation 1) , we get :
[tex][A] = 50\times e^{-1.21\times 10^{-4}\times 2292} = 37.89\ gm\\\\[/tex]
Hence, this is the required solution.
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