A certain radioactive sample decays for a time period equal to its mean life . Find (i) the fraction of the sample that disintegrates and (ii) the fraction of the sample that remains intact.

Explanation

Time of decay, `t=tau=(1)/(lambda)`
The fraction of sample that remains intact `=(N)/(N_(0))`
the fraction of sample that disintegrates `=[1-(N)/(N_(0))]`
Consider `N=N_(0)e^(-lambda t)`
`therefore (N)/(N_(0))=e^(-lambdat)=e^(-lambdaxx(1)/(2))=e^(-1)=(1)/(e)`
i.e., `(N)/(N_(0))=(1)/(e)=(1)/(2.718)=0.368`
Fraction of the sample that remain intact =0.368. Fraction of the sample that disintegrates `=1-0.368=0.632`.