What is the probability of a radioactive nucleus to survive one mean life:

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Question: Answered & Verified by Expert

What is the probability of a radioactive nucleus to survive one mean life:

PhysicsNuclear PhysicsNEET

Options:

A $\frac{1}{e}$
B $\frac{1}{e + 1}$
C $1 - \frac{1}{e}$
D $1 + \frac{1}{e}$

Solution:

2743 Upvotes Verified Answer

The correct answer is:

\frac{1}{e}

\frac{N}{N_{0}} = e^{- λ \times \frac{1}{λ}} = \frac{1}{e}

Probability to survive = \frac{No . of nucleous survived}{Total no . of Nucleous}

P = \frac{N_{0} e^{- ⋋ \times \frac{1}{⋋}}}{N_{0}} = \frac{1}{e}

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