To determine the half-life of a radioactive element, a student plots a graph of | d N(t) d t | versust. 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| = N= N₀ e^ - t Taking log both sides | d N d t |= ( N₀ )- t Hence, | d N d t | versus t graph is a straight line with slope - From the graph we can see that, = 1 2 =0.5 yr ⁻¹ Now applying the equation, aligned N & =N₀ e^ - t & =N₀ e^ -0.5 4.16 & =N₀ e^ -2.08 =0.125 N₀ & = N₀ 8 aligned ie, nuclei decreases by a factor of 8 . Hence the answer is 8 .