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CGPET 2021 Solved Paper
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© examsnet.com
Question : 70
Total: 150
A piece of wood when buried in Earth had
1
%
14
C
(
t
1
2
=
5760.
y
e
a
r
s
)
. Now as charcoal, it has only
0.25
%
14
C
. How long has the piece of wood been buried?
9133 years
11520 years
5760 years
17280 years
Validate
Solution:
(b) The half-life
t
1
2
of
C
14
is 5760 years.
Initial amount of
C
14
is
1
%
Final amount of
mathrm
C
14
is
0.25
%
k
=
2303
t
log
a
a
−
x
.........(i)
where,
k
=
rate constant,
a
=
initial amount of reactant,
a
−
x
=
amount left/final amount of reactant leftand
t
=
time taken.
Also,
k
=
0.6932
t
1
2
.........(ii)
From (i) and (ii),
0.6932
t
1
2
=
2.303
t
log
a
a
−
x
0.6932
5760
=
2303
t
log
1
0.25
⇒
t
=
2303
0.6932
5760
log
(
4
)
=
11520
y
r
© examsnet.com
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