Question

10 mg of carbon from living material produce 200 counts per minute due to a small proportion of radioactive isotope carbon 14. A piece of ancient wood of mass 10 mg is found to give 50 counts per minute. Assuming that carbon 14 content of the atmosphere has remained unchanged the estimated age of the wood sample is (Given half life of carbon is 5700 years)

(1) 1.41×10⁷ years 

(2) 1.41×10¹⁰ years 

(3) 1.41×10⁴ years 

(4) 1.41×10¹⁴ years

Answer 1

Correct option : (3) 1.41×10⁴ years

Explanation:

Since the amount of carbon–14 in atmosphere remain constant and a living matter acquires carbon from atmosphere, the count from a living matter represent the amount of carbon–14 present in atmosphere. The ancient wood which has now 50 counts per minute from 10 mg in the beginning must have the same count rate as from the living matter that is 200 count per minute from 10 mg. Thus the age of the ancient wood is the time in which the carbon–14 count has decreased from the initial value of 200 counts per minute from 10 mg to the find value of 50 counts per minute from 10 mg. Then λ the disintegration constants of C¹⁴ is given by