Carbon-14 is used to determine the age of ancient objects. if a sample today contains 0.060 g of carbon-14, how much carbon-14 must have been present in the sample 11,430 years ago? the half-life of carbon-14 is 5730 years.

Answer : 0.239 gram of carbon-14 must have been present in the sample 11,430 years ago.

Solution : Given,

As we know that the radioactive decays follow first order kinetics.

First, we have to calculate the rate constant of carbon-14.

Formula used :

Now put the value of half-life, we get the value of rate constant.

Now we have to calculate the original amount of carbon-14.

The expression for rate law for first order kinetics is given by :

where,

k = rate constant  =

t = time taken for decay process  = 11430 years

a = initial amount of the carbon-14 = ?

a - x = amount left after decay process  = 0.060 g

Putting values in above equation, we get the value of initial amount of carbon-14.

Therefore, 0.239 gram of carbon-14 must have been present in the sample 11,430 years ago.