If the number of nuclei of a radioactive substance becomes 1/e times – InterviewSolution

InterviewSolution

1.

If the number of nuclei of a radioactive substance becomes 1/e times the initial number in 10 days, what is the decay constant of the substance ?

Answer»

N(t) = N₀e^-λt

∴ In this case,

\(\cfrac{N(t)}{N_0}\) = \(\cfrac1e\) = e^-λt\(\cfrac1{e^{λt}}\)

∴ λt = 1

∴ The decay constant,

λ = \(\cfrac1t\) = \(\cfrac1{10}\) day^-1

= 0.1 day^-1

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