The graph shows the log of activity log R of a radioactive material as a function of time t in minutes. The half-life (in minute) for the decay is closest to

Step-by-step solution

Activity of a radioactive sample is given by R = - d N d t = - d d t N 0 e - λ t = λ N 0 · e - λ t So , log R = log λ N 0 + log e - λ t ⇒ log R = - λ t + log λ N 0 This equation is form of y = m x + C So, absolute value of slope of log R versus t graph gives decay constant λ . Now, from graph, We get, slope = 8 - 6 8 - 16 = 1 4 = λ So, half-life time period of sample is T 1 / 2 = log 2 λ = 0 . 693 1 / 4 ≈ 3 . 0 min