The normal activity of living carbon-containing matter is found tobe about 15 decays per minute for every gram of carbon. This activityarises from the small proportion of radioactive 146 C present with thestable carbon isotope 126 C . When the organism is dead, its interactionwith the atmosphere (which maintains the above equilibrium activity)ceases and its activity begins to drop. From the known half-life (5730years) of 146 C , and the measured activity, the age of the specimencan be approximately estimated. This is the principle of 146C dating used in archaeology. Suppose a specimen from Mohenjodaro givesan activity of 9 decays per minute per gram of carbon. Estimate theapproximate age of the Indus-Valley civilisation.
Given: The decay rate of living carbon containing matter is 15 decays / min , the half life of C 6 14 is 5730 years and the decays rate of the specimen from Mohenjodaro site is 9 decays / min .
The relation for decay constant is given as,
e − λ t = R R ′
Where, the decay rate of living carbon containing matter is R the time is t , the decay constant is λ and the decays rate of the specimen from Mohenjodaro site is R ′ .
By substituting the given values in the above formula, we get
e − λ t = 9 15 = 3 5 − λ t = log e ( 3 5 ) t = 0.5108 λ
We know that,
λ = 0.693 T 1 2
Where, the half life of C 6 14 is T 1 2 .
By substituting the given value in the above expression, we get
t = 0.5108 0.693 5730 = 4223.5 years
Thus, the approximate age of the Indus valley Civilization is 4223.5 years .
Given: The decay rate of living carbon containing matter is
The relation for decay constant is given as,
Where, the decay rate of living carbon containing matter is
By substituting the given values in the above formula, we get
We know that,
Where, the half life of
By substituting the given value in the above expression, we get
Thus, the approximate age of the Indus valley Civilization is
