Question

What is the probability of a radioactive nucleus to survive one mean life?
A. `(1)/(e )`
B. `1-(1)/(e )`
C. `(ln 2)/(e )`
D. `(ln 2)/(e )`

Answer 1

Correct Answer - A
Probability of survival for any nucleus at time `t` is
`P(N)/(N_(0))=(N_(0)r^(-lambdat))/(N_(0))=e^(-lambda t)` M
So, in one mean life, required probabiltiy is
`e^(-lambdax(1)/(lambda))=(1)/(e ),`