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The relation between half life (T) and decay constant (λ) is

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As per radiaoactive decay law, the radioactive decays per unit time are directly proportional to the total number of nuclei of radioactive compounds in the sample.

f the number of nuclei in a sample is N and the number of radioactive decays per unit time dt is dN then,

dNdt=−λN

Integrating both limits

∫NN0dNN=–λ t∫t0dt

Taking initial time t0=0 we have

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