To determine the half-life of a radioactive element, a student plots graph of ln d N ( t ) d t versus t . Here d N ( t ) d t is the rate of radioactive decay at time t . If the number of radioactive nuclei of this element decreases by a factor of p after 4 . 16 yr , the value of p is

Step-by-step solution

d N d t = |Activity of radioactive substance|     =   λ N   =   λ N 0 e - λ t       ( ∵   N   =   N 0 e - λ t ) Taking log both sides l n d N d t =   l n (   λ N 0 ) - λ t Hence, ln d N d t versus t graph is a straight line with slope- λ . From the graph, we can see that, λ = 1 2 = 0.5   y r - 1 Now applying the equation N   =   N 0   e - λ t = N 0   e - 0.5   × &#16