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An archeologist on a dig finds a fragment of an ancient
basketwoven from grass. Later, it is determined that the
carbon-14content of the grass in the basket is 9.93% that of
anequal carbon sample from present-day grass. What is the age of
thebasket?

Respuesta :

boffeemadrid

Answer:

19792.96488 years

Explanation:

[tex]\tau_{\dfrac{1}{2}}[/tex] = Half life of carbon-14 atom = 5730 years

Disintegration is given by

[tex]\lambda=\dfrac{ln2}{\tau_{\dfrac{1}{2}}}\\\Rightarrow \lambda=\dfrac{ln2}{5730}\\\Rightarrow \lambda=0.00012\ /years[/tex]

The distintegration constant

[tex]0.093N_0=N_0e^{-\lambda t}\\\Rightarrow 0.093N_0=N_0e^{-0.00012 t}\\\Rightarrow ln\dfrac{1}{0.093}=0.00012t\\\Rightarrow t=\dfrac{ ln\dfrac{1}{0.093}}{0.00012}\\\Rightarrow t=19792.96488\ years[/tex]

The age of the basket is 19792.96488 years

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