NCERT Class XII Chapter
Nuclei
Questions With Solutions
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Question : 8
Total: 31
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
C present with the stable carbon isotope
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
C , and the measured activity, the age of the specimen can be approximately estimated. This is the principle of
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.
Solution:
In order to estimate age, let us first find the activity ratio in form of time ‘t’.
Given normal activity,R 0 = 15 decays m i n – 1
Present activity, R = 9 decaysm i n – 1 ,
T 1 ∕ 2 = 5730 years
Since activity is proportional to the number of radioactive atoms, therefore,
=
=
= e − λ t or / 15 = e − λ t or e λ t =
Taking natural logarithm ,
log e e λ t = log e
or λt log e e = 2.303 log 10
= 2.303 × 0.2218
or t =
... (i) [Since log e e = 1]
Now we know, half life,T 1 ∕ 2 =
∴ t =
=
× T 1 ∕ 2 =
years = 4224 years
Given normal activity,
Present activity, R = 9 decays
Since activity is proportional to the number of radioactive atoms, therefore,
Taking natural logarithm ,
or t =
Now we know, half life,
∴ t =
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