# 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 - Physics

Numerical

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 ""_6^14"C" present with the stable carbon isotope ""_6^12"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 ""_6^14"C" and the measured activity, the age of the specimen can be approximately estimated. This is the principle of ""_6^14"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 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 ""_6^14"C", "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, λ and time, t as:

"N"/"N'" = "R"/"R'" = "e"^(-lambda"t")

"e"^(-lambda"t") = 9/15 = 3/5

-lambda"t" = 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 years

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

Concept: Law of Radioactive Decay
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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 13 Nuclei
Exercise | Q 13.8 | Page 462
NCERT Class 12 Physics Textbook
Chapter 13 Nuclei
Exercise | Q 8 | Page 462

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