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.
