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IIT JEE Advanced 2006 Paper 1
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© examsnet.com
Question : 69
Total: 120
A nuclear explosion has taken place leading to increase in the concentration of
C
14
in nearby areas.
C
14
concentration is
C
1
in nearby areas and
C
2
in areas far away. If the age of the fossil is determined to be
T
1
and
T
2
at the places respectively then
The age of the fossil will increase at the place where explosion has taken place and
T
1
−
T
2
=
1
λ
ln
C
1
C
2
.
The age of the fossil will decrease at the place where explosion has taken place and
T
1
−
T
2
=
1
λ
ln
C
1
C
2
.
The age of fossil will be determined to be the same.
T
1
T
2
=
C
1
C
2
.
Validate
Solution:
Radioactive decay of all elements follows first-order kinetics .So, in accordance with first-order kinetics, the decay constant is
λ =
1
T
1
−
T
2
ln
C
1
C
2
⇒
T
1
−
T
2
=
1
λ
ln
C
1
C
2
The rate of decay is proportional to the concentration, it would be faster near the explosion as concentration of
14
C
is more. Hence, the age of fossil will increase.
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