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12th Physics Notes - Law of Radioactive decay - JEE Main 2014 by ednexa.com

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- 1. Law of Radioactive decay 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. Derivation: Let N0 be the number of nuclei present at time t = 0 and N the number of nuclei present at time t. From the law of radioactive decay, dN N dt dN dt N dN N dt …(i) where, λ is a constant of proportionality called the radioactive decay constant or the disintegration constant. It is a constant for a particular radioactive element. The minus sign indicates that N decreases as t increases. Integrating equation (i),
- 2. N0 0 t t dN dt dt N 0 0 ∴ loge N – loge N0 = −λt N log e t N0 …(ii) N et N0 ∴ N = N0 e-λt …(iii) This is the exponential form of the law of radioactive decay. It shows that the number of nuclei present decreases exponentially with time. Keep on visiting www.ednexa.com For more information, please call 9011041155. - Team Ednexa

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