An ancient club is found that contains 200 g of pure carbon and has an activity of 7.5 decays per second. determine its age assuming that in living trees the ratio of ( 14 c 12 c ) ( 14 c 12 c ) atoms is about 1.10 × 10 − 12 1.10 × 10 − 12 . note that the half life of carbon-14 is 5700 years and the avogadro number is 6.02 × 10 23 6.02 × 10 23 .

Answer : The age will be, 14205.59 year

Explanation :

First we have to determine the decay constant (k).

Now we have to determine the number of nuclei.

Number of nuclei =

Number of nuclei =

Now we have to determine the number of nuclei.

Ratio of to =

Now we have to determine the initial activity.

conversion used :

Now we have to determine the current activity.

Now we have to determine its age.

Therefore, the age will be, 14205.59 year

this would be about 43%