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04(a) From the law of radioactive decay, show that thetotal rate of decay, R=Roe-t, where the symbolshave their usual meanings. |
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Answer» 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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