Answer:
Age of the piece of wood was found out to be 55,434.65 years
Step-by-step explanation:
The ratio of carbon-14 to carbon-12 in a piece of wood discovered in a cave is
[tex]=\dfrac{1}{816}[/tex]
i.e [tex]\dfrac{N}{N_0}=\dfrac{1}{816}[/tex]
We know that,
[tex]t=\dfrac{\ln \frac{N}{N_0}}{-0.693}\cdot t_{\frac{1}{2}}[/tex]
Where [tex]t_{\frac{1}{2}}[/tex] is the half-life of the isotope carbon 14, which is 5730 years.
Putting the values,
[tex]t=\dfrac{\ln \dfrac{1}{816}}{-0.693}\cdot 5730[/tex]
[tex]=\dfrac{-6.7044}{-0.693}\cdot 5730[/tex]
[tex]=\dfrac{6.7044\times 5730}{0.693}[/tex]
[tex]=55,434.65[/tex] years
