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

Options

A. `63%`
B. `69.3%`
C. `37%`
D. `50%`

Answer

A

Explanation

For radioactive decay, `(N)/(N_(0))=e^(-lambdat)`
where `N_(0)=` intial number of active nuclei and N = number of active nuclei left after the time t.
Here, t = mean life `=(1)/(lambda)(lambda" is decay constant")`
`(N)/(N_(0))=e^(-lambdaxx(1)/(lambda))=(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" Perecentage of decay "=(N_(0)-N)/(N_(0))xx100=63.2~=63%`