Question

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 1

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 :
`t_(1/2)=(0.693)/(k)`

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

`5730years=(0.693)/(k)`

`k=1.209* 10^(-4)year^(-1)`

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

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

`k=(2.303)/(t)\log(a)/(a-x)`

where,

k = rate constant =
`1.209* 10^(-4)year^(-1)`

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.

`1.209* 10^(-4)year^(-1)=(2.303)/(11430years)\log(a)/(0.060g)`

`a=0.238g`

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