04
(a) From the law of radioactive decay, show that the
total rate of decay, R=Roe-t, where the symbols
have their usual meanings.
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Answer:
Law of radioactive decay : At any instant, the rate of radioactive disintegration is directly proportional to the number of nuclei of the radioactive element present at that instant.
We know by radioactive decay law
dt
dN
∝N
or
dt
dN
=−λN
where λ is the constant of proportionality called radioactive decay constant. Let N
0
be the number of nuclei present at time t=0, and N the number of nuclei present at time t.
∫
N
0
N
N
dN
=−∫
0
t
λdt=−λ∫
0
t
dt
log
e
N−log
e
N
0
=−λt
log
e
(
N
0
N
)=−λt
N
0
N
=e
−λt
N=N
e
−λt
Explanation:
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