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Question

Physics Question on Nuclei

The probability of survival of a radioactive nucleus for one mean life is

A

1e\frac{1}{e}

B

1−1e1-\frac{1}{e}

C

1n2e\frac{1n 2}{e}

D

1−1n2e1-\frac{1n 2}{e}

Answer

1e\frac{1}{e}

Explanation

Solution

Probability of survival for any nucleus at time tt is P=NN0=N0e−λtN0=e−λtP = \frac{N}{N_0} = \frac{N_0 e^{- \lambda t}}{N_0} = e^{-\lambda t} So, in one mean life, required probability is e−λ=1λ=1ee^{- \lambda = \frac{1}{\lambda}} = \frac{1}{e}