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 146C present with the stable carbon isotope 126C . 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 146C, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of 146C 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.

Answer 1

Answer:

Decay rate R=15 decay/min

Let, N be number of radioactive atoms present.

Half-life of carbon, T=5730 years

Decay rate of specimen, R

′

=9 decay/min

Let N

′

be bumber of radioactive present in specimen.

as,

N

′

N

=

R

′

R

=e

−λt

So, t=0.5108/λ or λ=0.693/T

i.e., t=4223.5 years

Explanation:

Decay rate R=15 decay/min

Let, N be number of radioactive atoms present.

Half-life of carbon, T=5730 years

Decay rate of specimen, R

′

=9 decay/min

Let N

′

be bumber of radioactive present in specimen.

as,

N

′

N

=

R

′

R

=e

−λt

So, t=0.5108/λ or λ=0.693/T

i.e., t=4223.5 years