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NCERT Class XII Chapter
Nuclei
Questions With Solutions

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Question : 7
Total: 31
A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to (a) 3.125% (b) 1% of its original value?
Solution:  
Activity R = R0e−λt
Also instantaneous activity, R = – λN
R = -
0.693
T
 N
Initial activity, R0 = – λN0
So, R0 = -
0.693
T
N0
(a)
R
R0
 =
N
N0
 =
3.125
100
 =
1
32
 or
N
N0
 = (
1
2
)n = (
1
2
)5 or n = 5
∴ t = nT = 5T years.
(b)
R
R0
 =
N
N0
 = e−λt =
1
100
Required time, as cannot be solved by direct calculation as in part (a).
t =
2.303
λ
 log
N0
N
 =
2.303T
0.693
 log 100 =
2.303×2×T
0.693
 = 6.65 T years
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