To determine the half life of a radioactive element , a student plote a graph of in `|(dN(t))/(dt)| versus t , Here |(dN(t))/(dt)|` is the rate of radioatuion decay at time t , if the number of radoactive nuclei of this element decreases by a factor of p after `4.16 ` year the value of p is

Answer

`8`

Explanation

`|(dN)/(dt)|=lambdaN_(0)e^(-lambdat) :. ln |(dN)/(dt)|=ln(N_(0)lambda)-lambdat`
`:. ln |(dN)/(dt)|=ln (N_(0)lambda)-lambdatimplies -lambda=` slope `=-1/2year^(-1)`
`implies lambda=1/2 yr^(-1)`
`:. t_(1//2)=0.693/lambda=1.386` given time is `3` times of `t_(1//2)`
`:.` value of p is 8.