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`
`=(dN)/(dt)=lambdaN_(0)e^(-lambdat)`
`l n |(dN)/(dt)|= -lambdat+ l n(lambdaN_(0))`
`y=mx+c`
`m= -lambda`
`lambda=(1)/(2)` [slope by graph `=(1)/(2)`]
`T=( l n2)/(lambda)`
`=2xx0.693=(4.16)/(n)`
`n=3=`no. of half life.
`p=z^(3)=8`.