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Standard XII
Physics
Alpha Decay
The decay con...
Question
The decay constant of a radioactive sample is
λ
. The respective values of its half life and meanlife are
i)
1
λ
and
(
l
o
g
e
2
)
ii)
l
o
g
e
2
λ
and
1
λ
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Solution
We have decay equation as follows
Remaining nuclei ,
N
=
N
0
e
−
λ
t
..................(1)
We know that for
t
=
h
a
l
f
−
l
i
f
e
we get remaining nuclei as half of initial nuclei
(
N
0
)
i.e
N
=
N
0
/
2
so using this with
t
=
t
1
/
2
in equation-1 we get
t
1
/
2
=
l
o
g
e
2
λ
Mean life is nothing but time(T) for which
N
=
N
0
/
e
so using it in equation-1 we get
T
=
1
λ
Option 2 is correct.
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