Question

An archeologist on a dig finds a fragment of an ancient

Answer 1

Answer:

19792.96488 years

Explanation:

$\tau_{\dfrac{1}{2}}$ = Half life of carbon-14 atom = 5730 years

Disintegration is given by

$\lambda=\dfrac{ln2}{\tau_{\dfrac{1}{2}}}\\\Rightarrow \lambda=\dfrac{ln2}{5730}\\\Rightarrow \lambda=0.00012\ /years$

The distintegration constant

$0.093N_0=N_0e^{-\lambda t}\\\Rightarrow 0.093N_0=N_0e^{-0.00012 t}\\\Rightarrow ln\dfrac{1}{0.093}=0.00012t\\\Rightarrow t=\dfrac{ ln\dfrac{1}{0.093}}{0.00012}\\\Rightarrow t=19792.96488\ years$

The age of the basket is 19792.96488 years