Carbon-14 has a half-life of 5720 years and this is a first-order reaction. If a piece of wood has converted 88.5% of the carbon-14, then how old is it?

The sample of Carbon-14 isotope is 37056.3 years old

Explanation:

The equation used to calculate rate constant from given half life for first order kinetics:

where,

= half life of the reaction = 5720 years

Putting values in above equation, we get:

Rate law expression for first order kinetics is given by the equation:

where,

k = rate constant  =

t = time taken for decay process = ? yr

= initial amount of the sample = 100 grams

[A] = amount left after decay process =  (100 - 88.5) = 11.5 grams

Putting values in above equation, we get:

Hence, the sample of Carbon-14 isotope is 37056.3 years old