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Question

State radioactive decay law. Prove that radioactive decay is exponential in nature.

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Solution

Radioactive decay law states that the number of nuclei undergoing the decay per unit time is proportional to the total number of nuclei in the sample.

Radioactive decay law: N=N0eλt

PROVE:

dNdt=λN
dNN=λdt
logeN=λt+C

initial number of nuclei=N0
C=logeN0
loge(NN0)=λt
N=N0eλt

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