Answered

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The half-life of carbon 14 is 5, 730 years. How much would be left of an original 50-
gram sample after 2, 292 years?

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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