Question

If an ancient campfire were analyzed, was found to have only about one-eighth the carbon-14 that is normally found in living things, how long ago was that campfire extinguished? Answer in units of y.

Answer 1

• Half life time of Carbon 14 : $t_{1/2}}$ = 5730 years .
  

Radioactive decay : amount of radioactive carbon remain :

     
Since found carbon atom is 1/8 of normally found in living things it implies that :

N = No *el-In(2)#t)/t1/2

N/No = 1/8


and
(In (2)/1/2) = 0.0001209680943

so putting values in equation :

(1/8) = -0.0001209680943*t

so age of campfire :

t =17,190 years

So campfire has been extinguished for 17190 years .
Note : There is a simple trick to solve the problem that is since sample is 1/8 of normally found so it implies that sample ( campfire) has been gone through 3 half life time decay so it’s age : = (3 * half life time of C-14) =(3*5730 years ) = 17190 years