Carbon-14 has a half-life of 5720 years and this is a first order reaction. if a piece of wood has converted 75% of the carbon-14, then how old is it?

1145.8 years

Explanation:

Half-life of carbon-14 = 5720 years

First we have to calculate the rate constant, we use the formula :

Now we have to calculate the age of the sample:

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  =

t = age of sample  = ?

a = let initial amount of the reactant  = 100 g

x = amount decayed = 75 g

a - x = amount left after decay process  = 100 - 75 = 25g

Now put all the given values in above equation, we get