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What is the probability of a radioactive...

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

A

`(1)/(e)`

B

`1-(1)/(e)`

C

`(ln2)/(e)`

D

`1- (ln2)/(e)`

Text Solution

Verified by Experts

The correct Answer is:
a
Probability of survival for any nucleus at time t is
`P =(N)/(N_(0)) =(N_(0) e^(- lambda t))/(N_(0)) =e^(- lambda t)`
So, in one mean life, required probability is
`e^(- lambda xx (1)/(lambda)) =(1)/(e)`.
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