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
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.
Solution:  
In order to estimate age, let us first find the activity ratio in form of time ‘t’.
Given normal activity, R0 = 15 decays min1
Present activity, R = 9 decays min1,
T12 = 5730 years
Since activity is proportional to the number of radioactive atoms, therefore,
R
R0
=
N
N0
=
N0eλt
N0
= eλt or /15 = eλt or eλt =
15
9

Taking natural logarithm ,
logeeλt = loge
15
9
or λt loge e = 2.303 log10
5
3
= 2.303 × 0.2218
or t =
0.5109
λ
... (i) [Since loge e = 1]
Now we know, half life, T12 =
0.693
λ

∴ t =
0.5109
0.693T12
=
0.5109
0.693
×T12
=
0.5109×5730
0.693
years = 4224 years
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