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# The Normal Activity of Living Carbon-containing Matter is Found to Be About 15 Decays per Minute for Every Gram of Carbon Estimate the Approximate Age of the Indus-valley Civilisation. - Physics

#### Question

The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive ""_6^14C present with the stable carbon isotope ""_6^12C . When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life (5730 years) of ""_6^14C and the measured activity, the age of the specimen can be approximately estimated. This is the principle of ""_6^14C" dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.

#### Solution

Decay rate of living carbon-containing matter, R = 15 decay/min

Let N be the number of radioactive atoms present in a normal carbon- containing matter.

Half life of ""_6^14C T_(1/2)= 5730 years

The decay rate of the specimen obtained from the Mohenjodaro site:

R' = 9 decays/min

Let N' be the number of radioactive atoms present in the specimen during the Mohenjodaro period.

Therefore, we can relate the decay constant, λand time, t as:

N/N' = R/R' = e^(-lambdat)

e^(-lambdat) = 9/15 = 3/5

-lambdat = log_e 3/5 = -0.5108

:. t= 0.5108/lambda

But lambda = 0.639/T_"1/2" = 0.693/5730

:, t = 0.5108/(0.693/5730) = 4223.5 year

Hence, the approximate age of the Indus-Valley civilisation is 4223.5 years.

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