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Q. A sample of radioactive substance shows an activity of 3.4 millicurie and after 600 seconds the activity shown is 1.7 millicurie. What is the half-life of radioactive sample
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Answer:
r
1
=2.3×10
−3
curie
r
2
=1.62×10
−3
curie, when t = 600 s
∴
r
2
r
1
=
1.62×10
−3
2.3×10
−3
=
N
2
N
1
(∴r∝ Number of atoms)
K=
t
2.303
log
N
2
N
1
=
600
2.303
log
1.62
2.3
=5.84×10
−1
s
−1
∴t
1/2
=
K
0.693
=
5.84×10
−4
0.693
=1186.15s
T(average life) =
K
1
=
5.84×10
−4
1
= 1712.33 s
or,
T=1.44×t
1/2
=1.44×1186.15
= 1712.33 s
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