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

Options

A. 8
B. 4
C. 2
D. 16

Answer

A

Explanation

`(-dN)/(dt)=lamda N`
`rArr (-dN)/(dt) = lamda N_(0) e_(- lamda t)`
`l n|(dN)/(dt)|=- lamda t +l n(lamda N_(0))`
`y = mx +_c rArr m = - lamda` ltbr gt `lamda = (1)/(2)` [Slope by graph `= (1)/(2)`]
`T=(l n2)/(lamda) =2 xx 0.693 = (4.16)/(n)`
`n=3` =no . of half life
`p = z_(3)= 8`.