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Question

State the law of radioactive decay. Hence derive the expression N=N0eλt where symbols have their usual meanings.

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Solution

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
dNdtN
or dNdt=λN
where λ is the constant of proportionality called radioactive decay constant. Let N0 be the number of nuclei present at time t=0, and N the number of nuclei present at time t.
NN0dNN=t0λdt=λt0dt
logeNlogeN0=λt
loge(NN0)=λt
NN0=eλt
N=N0eλt
629870_601691_ans_9e81be998e924567b6d00569a91b43d3.png

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