Q. 84.4( 5 Votes )

# 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 ^{14}_{6}C present with the stable carbon isotope ^{12}_{6}C. 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 ^{14}_{6}C, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of ^{14}_{6}C 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 civilization.

Answer :

Let N be a number of radioactive carbon found in normal carbon and N_{0} be the number of radioactive carbon found in the specimen. The half-life of C-14 is 5730 yrs.

Decay rate of living carbon-containing matter = D = 15 decay/min-gm

Decay rate of the specimen at Mohenjo-Daro = D_{0} = 9 decays/min-gm

__From the exponential decay rate law, we get,__

∴ Hence,

So, -λt = ln(3/5) = -0.5108

t =

or, t =

Approximate age of Indus-Valley-Civilization is 4223.5 years.

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A charged capacitor of capacitance C is discharged through a resistance R. A radioactive sample decays with an average-life τ. Find the value of R for which the ratio of the electrostatic field energy stored in the capacitor to the activity of the radioactive sample remains constant in time.

HC Verma - Concepts of Physics Part 2