In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life?

Options

A. 0.63
B. 0.693
C. 0.37
D. 0.5

Answer

A

Explanation

We have for radioactive decay,
`(N)/(N_(0))=e^(-lamdat)`, where `N_(0)=`initial number of active nuclei and N=number of active nuclei after the mean life.
Here, t=mean life=`1//lamda` (`lamda` is decay constant).
`therefore(N)/(N_(0))=e^(-lamdaxx(1)/(lamda))=(1)/(e)`.
or, `1-(N)/(N_(0))=1-(1)/(e)=1-(1)/(2.718)=0.632`.
or, `(N_(0)-N)/(N_(0))=0.632`
`therefore` Percentage of decay
`=(N_(0)-N)/(N_(0))xx100=63.2cong63%`.